Question

Now that Yousef is retired, he farms as a hobby. He sells his produce at a weekly local farmers' market. This week, Yousef is harvesting tomatoes. He pays local students $2 per case to pick the tomatoes and has about $175 in weekly fixed costs for fuel, packaging, and other expenses. a. Using function notation, write a function for the total costs C, in dollars, for this week as a function of the number n, of cases of tomatoes picked. b. Yousef sells all of his tomatoes for $27 per case. Using function notation, write a function for the revenue R, in dollars, for this week as a function of n. c. Use the functions found in parts a and b to write a function for the profit P, in dollars, for this week as a function of n. Write in function notation and simplify the function. d. How many cases does Yousef need to sell to break even? Show your work.

Answer 1

Explanation:

let the number of cases be n

let the cost function be C(n)

the revenue function be R(n)

the profit function be P(n)

a. the cost for the week will be

C(n)= 175+2n

b. the cost of a case is $27

the revenue is

R(n)=27n

c. the profit is expressed as revenue - cost

P(n)= R(n)-C(n)

P(n)= 27n-(175+2n)

P(n)= 27n-175-2n

P(n)= 27n-2n-175

P(n)= 25n-175

d. break even point is the point at which total cost and total revenue are equal

C(n)=R(n

175+2n=27n

solving for n we have

175=27n-2n

175=25n

n=175/25

n=7