A local civic group is selling t-shirts to raise funds for Relay to Life. They plan to sell

2500 t-shirts for $10. They consider raising the t-shirt price in order to earn more

profit. For each $1 increase, they will sell 100 fewer t-shirts. Let x represent the

number of $1 increases.

a. Write a function,

Write a function, c (x), to represent the cost of one t-shirt based on the number

of increases.

b. Write a function, t (x), to represent the number of t-shirts sold based on the

number of increases.

c. Write a revenue function, r (x), for the t-shirt sell that could be used to maximize

Question

Mathematics

Marcel Alvarado

7 December, 15:19

A local civic group is selling t-shirts to raise funds for Relay to Life. They plan to sell

2500 t-shirts for $10. They consider raising the t-shirt price in order to earn more

profit. For each $1 increase, they will sell 100 fewer t-shirts. Let x represent the

number of $1 increases.

a. Write a function,

Write a function, c (x), to represent the cost of one t-shirt based on the number

of increases.

b. Write a function, t (x), to represent the number of t-shirts sold based on the

number of increases.

c. Write a revenue function, r (x), for the t-shirt sell that could be used to maximize

+3

Answers (1)

Know the Answer?

Brooklynn Blevins · Answer 1

a. Let us say that c (x) is the cost of one t shirt based on the number of increases therefore:

c = 10 + x

b. Say that t (x) is the number of t shirts sold based on the number of increases so:

t = 2500 - 100 x

b. The revenue is simply the product:

r (x) = (10 + x) (2500 - 100 x)

Combining:

r (x) = 25000 - 1000 x + 2500 x - 100 x^2

r (x) = 25000 + 1500 x - 100 x^2

Taking the 1st derivative and setting dr / dx = 0 to get the maxima:

dr / dx = 1500 - 200 x

1500 = 200 x

x = 7.5

t = 2500 - 100 x = 2500 - 100 (7.5) = 1750

Hence 1750 shirts should be sold.