At a selling price of GHC3.80 per unit, the expected sales of a particular product would be GHC10,200, but would fall to GHC8,400 if the selling price was GHC4.70. The total cost function

(GHC) for the product is 15000 + 1.8x where x is the number of units.

Required:

(a)

Derive the demand function, assuming it is linear.

(6 marks)

(b)

Derive an expression for total profit.

(6 marks)

(c)

Calculate the maximum profit and the level of sales at which the maximum is attained.

(6 marks)

(d)

What price is charged per unit at the maximum profit point​

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.