Functions : Maximizing Profit, Diminishing Returns and Maximizing Volume

1. The demand for a product in dollars is given by p(x) = 53/(x)^1/2 Fixed cost are $608 and the cost to produce each item is $0.53. Find the production level of x that maximizes profit within the range of 0<(or equal to)x< (or equal to)7530.

2. An efficiency study of the afternoon shift (12:00-4p.m.) at a factory shows that the average worker who starts at noon will have produced Q(t) units in t hours given by the formula: Q(t) = -t^3 + 9/2t^2 + 15t

At what time during the four-hour shift will the worker's production level reach the point of diminishing returns? At this time, how many units has the workers produced? What is the average production level for a worker over the four-hour shift?

3. An open box is made from cardboard by cutting out squares of equal size from the corners and then folding up the sides. Determine the volume of the largest box that can be constructed if the cardboard is originally 5 inches by 10 inches.

Solution Summary

Functions are used to maximize profit, analyze diminishing returns and maximize volume. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

Suppose the market price of sugar is 22 cents per pound. If a sugar farmer produces 100,000 pounds, the marginal cost of sugar is 30 cents per pound. Is the farmer maximizing profit? If not, should the farmer produce more or less sugar?

1. A profit-maximizing firm operating in a perfectly competitive market can sell products for $100 per unit. The firm has a cost function represented by:
C(Q) = 1000- 160Q + 10QSqr(10 q squared) . The market demand function for this product is Qd = 500 - 3P.
a.What is the profit maximizing output for this company?
b.Wh

The law of diminishing marginal returns states that
a. the marginal product of labor declines as all inputs are increased.
b. production functions exhibit decreasing returns to scale.
c. the marginal product of labor returns as more capital is used.
d. the marginal product of a factor eventually diminishes as more of the i

1. The following table shows data for a simple production function.
Capital(K) Labor(L) Total Product(TP) Average Product(AP) Marginal Product(MP)
Column 1 numbers = Capital ; Column 2 numbers = Labor; Column 3 numbers= Total Product
10 0 0

Under profit-maximizing equilibrium, which of the following will not be equal to the other three?
a) the marginal revenue product of input X.
b) The price of input X.
c) the marginal cost of input X.
d) the marginal product of input X.
e) all will be equal.

Carlton Industries, a manufacturer of electronic equipment, estimates the following relation between its marginal cost of production output:
MC = $150 + 0.005Q
a) What does this MC function imply about the effect of the law of diminishingreturns on Carlton's short-run cost function?
b) Derive the marginal cost of prod

In a monopoly with a 50-50 chance of a demand curve of P=20-Q or P=40-Q and MC=Q, what is the profit maximizing price. Please show the steps to find either $5, 10, 15, or 20.

Please refer attached file for diagram.
The follwing diagram shows the cost structure of a mononpoly firm as well as market demand. Identify on the graph and calculate the following:
a. Profit-maximizing output level
b. Profit-maximizing price
c. Total Revenue
d. Total Cost
e. Total profit or loss.
State the correct