Question

a baker rents space in a commercial kitchen for $200 per week. for each day he bakes, he spends $4 on materials. he charges $7.50 per pie. the graph below shows this baker’s costs and revenues for a week in which he sells p pies. how many pies must he sell in a week in order to break even? a. 20 b. 40 c. 60 d. he will never break even.

Explanation:

Step1: Define cost function

Let $p$ = number of pies.
Cost: $C(p) = 210 + 4p$

Step2: Define revenue function

Revenue: $R(p) = 7.50p$

Step3: Set cost = revenue (break-even)

$210 + 4p = 7.50p$

Step4: Solve for $p$

$210 = 7.50p - 4p$
$210 = 3.5p$
$p = \frac{210}{3.5} = 60$

Answer:

C. 60