Part One: Big-Foot’s Shoe Company makes extra large shoes for people with big feet. The target demographic for the company are people with shoe sizes over size 14. The company started in 2010, when Benjamin Bigfoot walked into a foot locker and could not find a big enough size for his feet. The company only sells one style of shoe in different sizes, which is Benjamin Bigfoot’s favorite type of shoe.

Part 2: The fixed costs include the start up costs to build the shoe factory ($25,000), the rent for the store ($5,000), and the costs of leather to make the extra large shoes ($20,000). The total fixed costs of the company is $50,000. The cost of producing one pair of Bigfoot’s shoes costs $5/pair. Bigfoot sells each pair of shoes for $25.

C(q)= 50,000 + 5q

R(q)= 25q

P(q)= (25q) – (50,000 + 5q)

 

Break Even Point Value : 25q= 50,000 + 5q   >>   20q=50,000    >>

q= 2500     >> 2500 shoes per month

Interpretation of graph: The break even point represents how many pairs of shoes Bigfoot’s needs to sell in order to make the same amount of money they are spending (breaking even). Every value to the right of the break even point represents profit, every value to the left represents a deficit.

The slope of the cost function represents the additional costs of the production of Bigfoot’s shoes. The slope of the revenue function represents the additional revenue Bigfoot’s makes for each pair of shoes sold.

Graph of Profit function

Interpretation of Profit graph

The profit function starts at the break even point of the Cost and Revenue functions and continues as a linear function after the point. The profit function represents the total profit that each unit yields.

Part 3

Quantity produced on a daily basis:  q= 100

The marginal cost for producing n=100 units would be $5

a(x)= C(q)/q =  >>     a(2500)= 50,000 + 5(2500)/2500 = 25

Average cost for the nth unit= $25

1. The marginal revenue is greater than the marginal cost at q=n. This is because the marginal revenue=R’(q) equals 25 and The marginal cost=C’(q), equals 5.

2.The number of units sold daily is 100 Pairs of Bigfoot shoes. 100 multiplied by 30 (to get the monthly rate), equals 3,000. This number is above the break even point, which is 2,500. Since this is above the break even point, the company will be making a profit every month. 

3.  R(101)-R(100)= 25(101)-25(100)=  25     C(101)-C(100)= (50,000 + 5(101))- (50,000+ 5(100))= 5

Yes, Bigfoot would still be making money by increasing q by 1, there will still be a profit of $20 on the additional unit. 

4. The average cost would decrease because the the fixed cost would be spread out and diluted more because of the additional units produced.

5.  Decreasing average costs helps the company. Lowering average costs allows more profit per unit because of lower costs.  

Part 4:

The company should thrive over the next 5 years based on the profit margin of the product that Bigfoot sells.  Decreasing average costs helps the company. This allows for more profit per unit sold due to a lower cost. So the more they sell, the more profit they will have.