Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Maximize C = subject to and a. What is the optimal value of x? X 14x + 13y + 5z 9x + 11y + 18z ≤ 61 14x + 15y + 12z ≤ 122 x ≥ 0, y z 0, z z 0. b. What is the optimal value of y? y Z c. What is the optimal value of z? d. What is the maximum value of the objective function?

6. The revenue function (in dollars) for a business is R(x)=-4x² +80x, and the cost function (in dollars) is C(x)=16x+26. Find the profit function, and then find the maximum profit. Max profit is $ 9866 2(-1) Max profit: 7. The cost and revenue functions for a business are given below. In each function, x is measured in ten-thousand units, and the function value is in millions of dollars. C(x)=x' + 2x² -5x+72 R(x)=x²-x²+25x a) Find the maximum profit, and the number of items produced and sold to generate that profit. and occurs when b) Find the number of units at which the business will break even. Max profit is $ 250 items are produced and sold. 8. A business' profit function is given by P(x)=-4x² +104x-640, where x is measured in hundreds of items, and the profit is in thousands of dollars. or and occurs when b) Find the number of units at which the business will break even. a) Find the maximum profit, and the number of items produced and sold to generate that profit. 25300 items…

a. The cost function of a firm is C (x) = x – 6x2 + 13x + 15 i. Derive an expression for the marginal cost ii. Find the value of x that minimizes the marginal cost function b. The production function of a firm is Y = AK 3 L3.Y represents output, K is capital, and L is labor. A is a constant term. This equation says that the firm uses labor and capital to produce its output. i. Find the marginal products of labor %3D ii. Find the marginal product of capital. C. A firm's revenue function is R (x) = 100x – 0.01a, and the cost function is C (x) = 50x + 10, 000, where x is output. a. Compute the marginal revenue function and the marginal cost function. b. Suppose the markets are competitive, which output level will maximize this firm's profit? Show all your calculations.

A company makes solar panels. The company's revenue function, in dollars, is R(n)=10n, where n is the number of panels produced. The cost function is C(n) = 100(2)0 . R and Care shown on the graph below. 1000 800 600 400 200 100 in 20 Number of Panels 0. 40 60 80 a) Estimate from the graph i) the break-even points ii) the number of panels that should be produced for maximum profit b) Write the equation for the profit function P. c) Graph P. d) Use your graph of P to estimate the number of panels that give maximum profit. e) How would your answers for break-even points and maximum profit change if i) the number of dollars of revenue per panel is increased slightly? i) the cost function is changed to C(n) = 100(2)s ? f) What does the number that was ch part e) i) represent? English (United States) OFocus Dollars