Mathematics: Alocal 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.

72Step-by-step explanation:8 times 9 equals 72...

Alocal civic group is selling t-shirts to raise funds

carolinehodges

12.03.2022

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.

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