Project

Business and Economics Aplications: Marginal Analysis

Maximizing Profit

An appliance firm is marketing a new refrigerator. It determines that in order to sell x refrigerators the price per refrigerator must be

It also determines that the total cost of producing x refrigerators is given by

(a)

Find the total revenue

(b) Graph the cost and the revenue (in the same frame) and find break-even points from the graphs.

(c) Estimates from graphs:

From the graphs, estimate the number of refrigerators the company must produce and

sell in order to maximize profit. Estimate this maximum profit from the graphs.

(i) number of refrigerators:____________________________

(ii) maximum profit: _________________________________

(d) Verification of the estimates obtained in (c) using Maximum - Minimum

Principles:

(i) Find the total profit :_________________________________

(ii) Find the critical point of :____________________________

[Compare your answer here to your answer in (c) (i) ]

(iii) Use the 2^nd Derivative Test to determine whether you have a maximum or a

minimum at the critical point.

(iv) Find the maximum( or minimum) value of the Profit at the critical.

[ Compare your answer here to your answer in (c) (ii)]

(e) Marginal Analysis

(i) Find the marginal cost .

(ii) Find the marginal revenue .

(iii) Find the value of x for which the marginal cost is equal to the marginal revenue.

[Compare your answer here to your answers in (c) (i) and (d) (ii) ]

(iv) Use the value of x obtained in (e) (iii) in the Profit-function to find the

corresponding profit.

[Compare your answer here to your answers in (c) (ii) and (d) (iv) ]