math

B O B B G E B G E C A O N - T H E - G O

Math 110 Project: Summer 2020?

Francisco Sandoval

Introduction and Assumptions Bobs Burgers, Burgers ON-THE-GO sells delicious hamburgers. In this report, I will find the cost to make and serve Bob B rger !

The following are the assumptions used figures the cost and revenue model for my micro-business

x Lets assume Q is the number of hamburgers sold x Lets assume p is the price of one hamburger x Here R (Q) refers to the total revenue x Here VC refers to the variable cost of one hamburger x Here TC (Q) refers to the total cost for operating business x Here P (Q) refers to the profit of business (R (Q) TC)

1. Total Revenue First, we find the revenue function. We assume that the selling price of one Bobs burger is 5 dollars (current data)

For the total revenue function

TR= Price x Quantity

TR = 5Q

The revenue function shows the number of hamburgers. One hamburger is $5 assume we sell 20 hamburgers - our revenue will be $100.

2. Total Cost: Now, we find the total cost function. But first we need to find the variable costs of catsup, mustard, relish, onions, etc. this will be added to the price of hamburgers sold.

The variable cost of EACH hamburger is $1.86 per.

This Forbes visual shows the per-burger variable cost of which is: $1.86.

The following bit is the Fixed cost of ONE hamburger. This value does not depend on the number of Hamburgers sold. The (fixed) cost will be same regardless of how many hamburgers are sold during business hours.

Fixed Costs:

Cost of Cart $2000

Cost of serving items (napkins, serving trays, utensils)

$300

Worker Salary (Bi-Weekly) $900

Utility cost (Electricity and gas) $250

Miscellaneous Costs $500

Total Fixed Costs $3950

The total fixed costs according to current data will be $3950 This includes the Cost of Cart, Cost of serving items, Worker Salary (Bi-Weekly), Utility costs (Electricity and gas) and Miscellaneous Costs

The total cost is the sum of the fixed and variable costs.

TC = FC + VC

TC= 3950 +1.86Q

3. Total Profit: Now to calculate the profit function it is simply the revenue minus total cost that will show the real income after deducting the all expenses

For Profit function:

P (Q) = 5Q (3950 +1.86Q)

P (Q) = 3.14Q 3950

4. Marginal Cost: The marginal cost Function shows the extra per dollar cost for producing the extra unit of product so here it shows how much it cost the for producing each extra unit of the hamburger. My total cost function will be telling me about the overall cost of the hamburgers I sold but the marginal cost will show me the cost of each additional unit of the hamburgers I produce.

Marginal cost = Change total cost / Change in quantity

So it is simply derivation = dC/ dQ = 1.86

5. Marginal Profit: The marginal profit function shows the extra per dollar value for selling an extra unit. Here it shows how much profit will come from the sale of each additional unit (Burgers). The total profit function will tell me the overall profit from the hamburgers sold but the marginal cost will show the cost of each additional unit sold.

Marginal profit = Change total profit/ Change in quantity

So it is simply derivation = dP/ dQ = 3.14

6. Breakeven Point: The breakeven point is when the cart makes no profit nor has a net-loss it shows the value where the total revenue equates to the total cost. After we surpass the breakeven point, the Burger cart will bring a profit (ideally).

Breakeven point:

TC = TR

3950+1.86Q = 5Q

3.14Q = 3950

Q = 1258 units of hamburgers

if 1258 hamburgers are sold. We will be at the breakeven point. If we sell more than 1258 hamburgers, a profit will show on our balance sheet.

7. Breakeven Point Graph The graph is thanks to Desmos. The horizontal axis shows the number of hamburgers sold; The

vertical axis shows total revenue // total cost. There are two linear graphs, the red line shows the

total revenue and the blue line shows the total cost function. Where both lines intersect is what I

like to call the breakeven point. The breakeven point is the 1258 hamburgers sold that gives the

cart $6290 in revenue.

References:

-The incredible hamburger visual https://www.forbes.com/sites/priceonomics/2017/04/07/how-much- do-the-ingredients-cost-in-your-favorite-foods/#554379e811ed

-Desmos