Calculus
SOLUTION: MATH 107 City College of San Francisco Marginal Costs of Setting up A Food Cart Paper
SOLUTION: MATH 107 City College of San Francisco Marginal Costs of Setting up A Food Cart Paper.
Math 110 Project
Spring 2022
For this project, you will research setting up a food cart that sells one item (like hot
dogs in buns) along with any condiments (like catsup, mustard, relish, onions, etc.) and
necessary serving products (like napkins, plates, containers/wrapping foil, etc.) You
may pick any food item of your choice. You will determine your total cost function,
revenue function, profit function, and find your break-even point(s).
Your project should contain all of the following elements:
1. Variable(s): Very clearly define your variable(s) and be specific. For example, if you say “?
represents hot dogs”, you will get very little credit. Does ? represent the number of hotdogs?
pounds of hotdogs? packages of hotdogs? dozens of hotdogs?
2. Total Cost: Research and determine your total cost function. Your cost function should
include the cost of the cart, cost of paying employees, cost of the food and supplies for the cart,
etc. Fully explain how you arrived at your cost function. Provide information/links in how you
determined what your supplies and materials cost. (You may ignore the cost of permits, taxes,
and city fees.)
3. Marginal Cost: Determine your marginal cost function. In your own words, explain what your
marginal cost function tells you. How is this different from what your total cost function tells
you?
4. Revenue: Determine your revenue function. Explain how you arrived at this function.
5. Profit: Determine your profit function. Explain how you arrived at this function.
6. Marginal Profit: Determine your marginal profit function. In your own words, explain what
your marginal profit function tells you. How is this different from what your profit function tells
you?
7. Break-Even: Find your break-even point(s) algebraically. Show all your work and explain your
reasoning.
8. Break-Even: Find your break-even point(s) graphically. The axes on your graphs should be
properly titled and labeled. So that your project looks professional, use software (such as
Desmos) to create your graphs. Show your work and explain your reasoning.
Type your project and save it to a PDF(prefer). Upload your PDF(prefer) to the “Final Project”
assignment in the Week 15 block on iLearn by the due date and time. iLearn will only accept
PDF(prefer) and Word files.
More detailed and well-researched projects with expanded explanations will receive higher
grades!
Crepe’y Delights
COMPANY OVERVIEW
Crepe’ y Delights is a Food Cart that specializes in the creation of custom, made to order crepes. We encourage
our consumers to enjoy the beauty of Southern Marin while eating one of our sweet or savory custom crepes. We
want to provide a product that is easily accessible and not overly crowded, as is the case with many of the existing
sit-in eateries in the area. We want to bring good feelings and full bellies to all residents and visitors of the
Southern Marin area while always seeking new ingredients and ideas for our crepes.
x Company Summary: Crepe’ y Delights specializes in fast custom crepes that have a low production cost and high
retail value. And as a Food cart, we can move with the crowds into parks or businesses at a significantly lower
price than a food truck.
x Markets and Products: Our market is the southern Marin area, a heavily visited area and popular walking, hiking,
boating, and biking area. However, most eateries in the area are sit down restaurants and tend to fill quickly.
Our product will specifically target breakfast and dinner customers that want to enjoy their day without
1
spending half it waiting in a line. We will initially offer a basic crepe with a variety of fruit, dairy, and protein
toppings, as time and goes on; our selection will expand to include more varied choices.
x Locations and Facilities: We are a single Food Cart that is able to go to areas that would otherwise be inaccessible
to food trucks. For storage and preparation, we are able to use our private residence, which saves significantly
on storage and facility costs, something that is not always a possibility with a food truck.
PRODUCT DESCRIPTION
x Product Overview: We will be selling crepes that customers can customize by selecting available toppings that
will vary on a weekly and monthly basis.
o Our initial offerings will be focused on fruit and dairy-based toppings, but plan on moving into more
unusual toppings as we build our customer base.
o
We will also be offering limited savory offerings. x Pricing: Our pricing will be based around the base cost
of a crepe that will increase based on the number of toppings the customer requests. Toppings will use a
1.5 tablespoon to identify the number of toppings used.
OPERATING PLAN
x
Payment: We plan on embracing a mostly electronic payment system; as such, we will make extensive use of
the Square POS technology with a small reserve of small bills to accommodate all customers.
x Technology: We plan on utilizing social media to reach out to customers to help plan our menu and create buzz
and a strong customer base.
x Key Customers: Our initial customers will be the visitors who come to southern Marin for biking and hiking and
walking the shoreline paths. These customers desire fast, affordable quality food with our getting stuck in a
line.
Costs and Pricing
x
Projected Start-Up and recurring Costs: The table below shows a sample of the recurring (variable) and
onetime (fixed) cost items to open your business.
Items
Cost
Amt/Month
Total Cost
Toppings
Peanut Butter (48 oz x2)
$10.69
2
$21.38
Nutella (33.5 oz x2)
Bananas (3 Ibs)
Strawberries (2 Ibs)
Peaches (5 Ibs)
Fuji Apples (5.5 Ibs)
Raspberries (12 oz)
$14.19
$2.99
$5.99
$9.99
$5.49
$6.49
2
2
4
4
2
4
$28.38
$5.98
$23.96
$39.96
$10.98
$25.96
Mangos (6 Ibs)
TOTALS
$7.49
2
$14.98
$171.58
$2.99
$14.99
3
2
$8.97
$29.98
Condiments
Yogurt (32 oz)
Caramel (90.4 oz)
2
Sweetened Condensed Milk (14oz x6)
Whipped cream (half Gallon)
Confectioners Powdered Sugar (50 Ibs)
Cinnamon (10.7 oz)
Cream Cheese (3 Ibs)
Maple syrup (33.8 Oz)
TOTALS
$11.69
$8.29
$33.19
$5.09
$8.19
$13.19
2
3
1
3
1
2
$23.38
$24.87
$33.19
$15.27
$8.19
$26.38
$170.23
$6.74
$14.99
$14.99
$18.09
6
4
6
8
$40.44
$59.96
$89.94
$144.72
$335.06
$85.00
$100.00
$16.00
1
2
4
$85.00
$200.00
$64.00
$349.00
Beverage
Nestle Bottled Water (16.9 oz x 35)
Coke (12 oz x 35)
Diet Coke (12 oz x35)
Starbucks Frap. Coffee Drink (9.5 oz x 15)
TOTALS
Operating Costs
Cellular/Wi-Fi
Gas (~$3.00/Gallon)
Propane
TOTALS
All Totals
Items
$1,025.87
Cost
Amt/3 Months
Total Cost
$20.99
$7.19
$13.09
$7.59
$16.19
$62.99
$28.59
$6.69
2
3
1
3
1
1
1
1
$41.98
$21.57
$13.09
$22.77
$16.19
$62.99
$28.59
$6.69
$213.87
$19.49
$24.49
$13.29
$16.69
$39.89
$19.99
4
4
5
3
4
4
$97.96
$53.16
$83.45
$119.67
$79.96
$84.76
Ingredients
Egg (15 Dozen)
Almond Milk (64 oz x3)
Flour (50 Ibs)
Whole Milk (2 Gallon x2)
Sugar (25 Ibs)
Butter (1 Ib x 30)
Vanilla (16 oz)
Salt (25 Ibs)
TOTALS
Materials
Container (6′ x 100)
Container (8×8″ x100)
Packaging Foil (x500)
Gloves (x100)
Dixie Napkin (1 Ply x 10000)
Vital Cutlery Kit (x 250)
3
Paper Towels (x 12)
Hand Soap (80 oz x2)
Face Mask (x 50)
Trash Bags (33 Gallons x 90)
Disinfecting wipes (x425)
Sponges (x21)
Glass Cleaner (32 oz x 4)
Dish Soap (90 oz)
TOTALS
$21.19
$10.69
$17.99
$19.09
$16.99
$15.69
$14.69
$9.89
2
1
5
2
3
1
1
1
$21.38
$17.99
$95.45
$33.98
$47.07
$14.69
$9.89
$9.89
$769.30
All Totals
Machinery
$983.17
Non-Recurring Costs
Cart
$1,900.00
Crepe Maker Iron Plates
$1,600.00
Generator
$1,381.92
Worktable
$103.99
*Point of Sale System
$0.00
Storage Bin (27 Gallon x3)
$31.47
iPad
799.99
Hauling Cooler
$399.99
TOTALS
$6,217.36
*2.6%x+.10
Menu Items
Price
Crepe
$5.00
Nestle Bottled Water (16.9 oz)
$1.15
Coke (12 oz)
$1.60
Diet Coke (12 oz)
$1.60
Starbucks Frap. Coffee Drink (9.5 oz)
$2.15
4
Topping
Price/Scoop
Fruit Toppings
$0.50
Yogurt
$0.75
Caramel
$0.75
Sweetened Condensed Milk
$0.75
Whipped cream
$0.50
Cream Cheese
$0.75
Projected Profit and Cost Model
Due to the reliance on bulk purchases and the necessity for the purchase of weekly fresh toppings (summed up
as monthly expenses), the costs will be based on the quarterly totals.
x
The projected cost model would be:
o 3(1025.87x) + 983.17x = C(x) o The
projected marginal cost would be:
4060.78 = MC
This seems to indicate that costs will always be fixed.
x
The projected Revenue model would be:
o 5x + 0.50a + .75b + .75c + .75d + .50e + .75f + 1.15g + 1.60h 2 + 2.15i – (.026x + .10) = R(x) o A
separate quantity is necessary to account for the separate toppings that may be selected.
o The PoS makes a profit based on the number of payments received.
x
The projected Profit model would be:
o (3(1025.87x) + 983.17x – 5x + 0.50a + .75b + .75c + .75d + .50e + .75f + 1.15g + 1.60h2 + 2.15i – (.026x +
.10) = P(x) x For an estimate of the profit using the
following model:
o 4060.78 – (12.30+3.2h) – (.026) = MP
o The marginal profit does consolidate the quantities that would otherwise be separated and does
eliminate the ability to see what toppings are the most used.
Break-Even Model
0.50a+.75b+.75c+.75d+.50e+.75f+1.15g+1.60h2+2.15i
5
=
31236.77x-.10
Purchase answer to see full
attachment
Spring 2022
For this project, you will research setting up a food cart that sells one item (like hot
dogs in buns) along with any condiments (like catsup, mustard, relish, onions, etc.) and
necessary serving products (like napkins, plates, containers/wrapping foil, etc.) You
may pick any food item of your choice. You will determine your total cost function,
revenue function, profit function, and find your break-even point(s).
Your project should contain all of the following elements:
1. Variable(s): Very clearly define your variable(s) and be specific. For example, if you say “?
represents hot dogs”, you will get very little credit. Does ? represent the number of hotdogs?
pounds of hotdogs? packages of hotdogs? dozens of hotdogs?
2. Total Cost: Research and determine your total cost function. Your cost function should
include the cost of the cart, cost of paying employees, cost of the food and supplies for the cart,
etc. Fully explain how you arrived at your cost function. Provide information/links in how you
determined what your supplies and materials cost. (You may ignore the cost of permits, taxes,
and city fees.)
3. Marginal Cost: Determine your marginal cost function. In your own words, explain what your
marginal cost function tells you. How is this different from what your total cost function tells
you?
4. Revenue: Determine your revenue function. Explain how you arrived at this function.
5. Profit: Determine your profit function. Explain how you arrived at this function.
6. Marginal Profit: Determine your marginal profit function. In your own words, explain what
your marginal profit function tells you. How is this different from what your profit function tells
you?
7. Break-Even: Find your break-even point(s) algebraically. Show all your work and explain your
reasoning.
8. Break-Even: Find your break-even point(s) graphically. The axes on your graphs should be
properly titled and labeled. So that your project looks professional, use software (such as
Desmos) to create your graphs. Show your work and explain your reasoning.
Type your project and save it to a PDF(prefer). Upload your PDF(prefer) to the “Final Project”
assignment in the Week 15 block on iLearn by the due date and time. iLearn will only accept
PDF(prefer) and Word files.
More detailed and well-researched projects with expanded explanations will receive higher
grades!
Crepe’y Delights
COMPANY OVERVIEW
Crepe’ y Delights is a Food Cart that specializes in the creation of custom, made to order crepes. We encourage
our consumers to enjoy the beauty of Southern Marin while eating one of our sweet or savory custom crepes. We
want to provide a product that is easily accessible and not overly crowded, as is the case with many of the existing
sit-in eateries in the area. We want to bring good feelings and full bellies to all residents and visitors of the
Southern Marin area while always seeking new ingredients and ideas for our crepes.
x Company Summary: Crepe’ y Delights specializes in fast custom crepes that have a low production cost and high
retail value. And as a Food cart, we can move with the crowds into parks or businesses at a significantly lower
price than a food truck.
x Markets and Products: Our market is the southern Marin area, a heavily visited area and popular walking, hiking,
boating, and biking area. However, most eateries in the area are sit down restaurants and tend to fill quickly.
Our product will specifically target breakfast and dinner customers that want to enjoy their day without
1
spending half it waiting in a line. We will initially offer a basic crepe with a variety of fruit, dairy, and protein
toppings, as time and goes on; our selection will expand to include more varied choices.
x Locations and Facilities: We are a single Food Cart that is able to go to areas that would otherwise be inaccessible
to food trucks. For storage and preparation, we are able to use our private residence, which saves significantly
on storage and facility costs, something that is not always a possibility with a food truck.
PRODUCT DESCRIPTION
x Product Overview: We will be selling crepes that customers can customize by selecting available toppings that
will vary on a weekly and monthly basis.
o Our initial offerings will be focused on fruit and dairy-based toppings, but plan on moving into more
unusual toppings as we build our customer base.
o
We will also be offering limited savory offerings. x Pricing: Our pricing will be based around the base cost
of a crepe that will increase based on the number of toppings the customer requests. Toppings will use a
1.5 tablespoon to identify the number of toppings used.
OPERATING PLAN
x
Payment: We plan on embracing a mostly electronic payment system; as such, we will make extensive use of
the Square POS technology with a small reserve of small bills to accommodate all customers.
x Technology: We plan on utilizing social media to reach out to customers to help plan our menu and create buzz
and a strong customer base.
x Key Customers: Our initial customers will be the visitors who come to southern Marin for biking and hiking and
walking the shoreline paths. These customers desire fast, affordable quality food with our getting stuck in a
line.
Costs and Pricing
x
Projected Start-Up and recurring Costs: The table below shows a sample of the recurring (variable) and
onetime (fixed) cost items to open your business.
Items
Cost
Amt/Month
Total Cost
Toppings
Peanut Butter (48 oz x2)
$10.69
2
$21.38
Nutella (33.5 oz x2)
Bananas (3 Ibs)
Strawberries (2 Ibs)
Peaches (5 Ibs)
Fuji Apples (5.5 Ibs)
Raspberries (12 oz)
$14.19
$2.99
$5.99
$9.99
$5.49
$6.49
2
2
4
4
2
4
$28.38
$5.98
$23.96
$39.96
$10.98
$25.96
Mangos (6 Ibs)
TOTALS
$7.49
2
$14.98
$171.58
$2.99
$14.99
3
2
$8.97
$29.98
Condiments
Yogurt (32 oz)
Caramel (90.4 oz)
2
Sweetened Condensed Milk (14oz x6)
Whipped cream (half Gallon)
Confectioners Powdered Sugar (50 Ibs)
Cinnamon (10.7 oz)
Cream Cheese (3 Ibs)
Maple syrup (33.8 Oz)
TOTALS
$11.69
$8.29
$33.19
$5.09
$8.19
$13.19
2
3
1
3
1
2
$23.38
$24.87
$33.19
$15.27
$8.19
$26.38
$170.23
$6.74
$14.99
$14.99
$18.09
6
4
6
8
$40.44
$59.96
$89.94
$144.72
$335.06
$85.00
$100.00
$16.00
1
2
4
$85.00
$200.00
$64.00
$349.00
Beverage
Nestle Bottled Water (16.9 oz x 35)
Coke (12 oz x 35)
Diet Coke (12 oz x35)
Starbucks Frap. Coffee Drink (9.5 oz x 15)
TOTALS
Operating Costs
Cellular/Wi-Fi
Gas (~$3.00/Gallon)
Propane
TOTALS
All Totals
Items
$1,025.87
Cost
Amt/3 Months
Total Cost
$20.99
$7.19
$13.09
$7.59
$16.19
$62.99
$28.59
$6.69
2
3
1
3
1
1
1
1
$41.98
$21.57
$13.09
$22.77
$16.19
$62.99
$28.59
$6.69
$213.87
$19.49
$24.49
$13.29
$16.69
$39.89
$19.99
4
4
5
3
4
4
$97.96
$53.16
$83.45
$119.67
$79.96
$84.76
Ingredients
Egg (15 Dozen)
Almond Milk (64 oz x3)
Flour (50 Ibs)
Whole Milk (2 Gallon x2)
Sugar (25 Ibs)
Butter (1 Ib x 30)
Vanilla (16 oz)
Salt (25 Ibs)
TOTALS
Materials
Container (6′ x 100)
Container (8×8″ x100)
Packaging Foil (x500)
Gloves (x100)
Dixie Napkin (1 Ply x 10000)
Vital Cutlery Kit (x 250)
3
Paper Towels (x 12)
Hand Soap (80 oz x2)
Face Mask (x 50)
Trash Bags (33 Gallons x 90)
Disinfecting wipes (x425)
Sponges (x21)
Glass Cleaner (32 oz x 4)
Dish Soap (90 oz)
TOTALS
$21.19
$10.69
$17.99
$19.09
$16.99
$15.69
$14.69
$9.89
2
1
5
2
3
1
1
1
$21.38
$17.99
$95.45
$33.98
$47.07
$14.69
$9.89
$9.89
$769.30
All Totals
Machinery
$983.17
Non-Recurring Costs
Cart
$1,900.00
Crepe Maker Iron Plates
$1,600.00
Generator
$1,381.92
Worktable
$103.99
*Point of Sale System
$0.00
Storage Bin (27 Gallon x3)
$31.47
iPad
799.99
Hauling Cooler
$399.99
TOTALS
$6,217.36
*2.6%x+.10
Menu Items
Price
Crepe
$5.00
Nestle Bottled Water (16.9 oz)
$1.15
Coke (12 oz)
$1.60
Diet Coke (12 oz)
$1.60
Starbucks Frap. Coffee Drink (9.5 oz)
$2.15
4
Topping
Price/Scoop
Fruit Toppings
$0.50
Yogurt
$0.75
Caramel
$0.75
Sweetened Condensed Milk
$0.75
Whipped cream
$0.50
Cream Cheese
$0.75
Projected Profit and Cost Model
Due to the reliance on bulk purchases and the necessity for the purchase of weekly fresh toppings (summed up
as monthly expenses), the costs will be based on the quarterly totals.
x
The projected cost model would be:
o 3(1025.87x) + 983.17x = C(x) o The
projected marginal cost would be:
4060.78 = MC
This seems to indicate that costs will always be fixed.
x
The projected Revenue model would be:
o 5x + 0.50a + .75b + .75c + .75d + .50e + .75f + 1.15g + 1.60h 2 + 2.15i – (.026x + .10) = R(x) o A
separate quantity is necessary to account for the separate toppings that may be selected.
o The PoS makes a profit based on the number of payments received.
x
The projected Profit model would be:
o (3(1025.87x) + 983.17x – 5x + 0.50a + .75b + .75c + .75d + .50e + .75f + 1.15g + 1.60h2 + 2.15i – (.026x +
.10) = P(x) x For an estimate of the profit using the
following model:
o 4060.78 – (12.30+3.2h) – (.026) = MP
o The marginal profit does consolidate the quantities that would otherwise be separated and does
eliminate the ability to see what toppings are the most used.
Break-Even Model
0.50a+.75b+.75c+.75d+.50e+.75f+1.15g+1.60h2+2.15i
5
=
31236.77x-.10
Purchase answer to see full
attachment
SOLUTION: MATH 107 City College of San Francisco Marginal Costs of Setting up A Food Cart Paper