A local civic group is selling t-shirts to raise funds for Relay to Life. They plan to sell2500 t-shirts for $10. They consider raising the t-shirt price in order to earn moreprofit. For each $1 increase, they will sell 100 fewer t-shirts. Let x represent thenumber of $1 increases.a. Write a function,Write a function, c(x), to represent the cost of one t-shirt based on the numberof increases.b. Write a function, t(x), to represent the number of t-shirts sold based on thenumber of increases.c. Write a revenue function, r(x), for the t-shirt sell that could be used to maximize

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.