A product plant is being considered for a new booming market. Total fixed cost for design, land, and plant construction is $105. The variable cost of producing product is a function C (n) = 100n - 3 x 10-3 n2 + 10-7 n3 where n = number of product produced.
(a) Determine the total cost function C (T). (Hint: It includes the cost of producing the product and fixed cost.)
(b) Find the marginal cost function Cm for producing the product.
(c) Find the number of product for minimum marginal cost. What is the marginal cost at this point? What is the average cost per unit at this level of production?
(d) Total revenue is given by S (n) = 250 n. Find the marginal price. Determine the functions for total profit, and marginal profit.
(e) Find the point to maximize profit.
(f) Graph these cost equations.
The solution determines a cost estimating function.