Question

A clothing manufacturer offers a discount on the unit price P, in euros (€), off its shirts based on the number of shirts purchased, s.

P'(s) = -0.004s is the function that gives the rate of change in the unit price of the shirts, and 9 shirts cost €9.75 each.

How much would each shirt cost if a clothing retailer purchased 40 for sale in their store?

a) €9.75
b) €10.35
c) €10.95
d) €11.55

Answer 1

The cost of each shirt would be approximately €8.63.

Step-by-step explanation:

To find the cost of each shirt when purchasing 40 shirts, we can use the function given: P'(s) = -0.004s, where s is the number of shirts purchased. We are given that 9 shirts cost €9.75 each, so we can substitute s = 9 and P = 9.75 into the function to find the rate of change in the unit price: P'(9) = -0.004(9) = -0.036.

To find the cost of each shirt when purchasing 40 shirts, we can multiply the rate of change by the number of additional shirts from 9 to 40: -0.036(40-9) = -0.036(31) = -1.116.

To find the new unit price, subtract the rate of change from the original cost of each shirt: 9.75 - 1.116 = 8.634. Therefore, each shirt would cost approximately €8.63.