Chapter 14.4, Problem 26E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Profit** Suppose that a firm produces two products,

To determine

**To prove:** The profit from the products, *A* and *B*, is maximized, when *A* and *B* is

Explanation

**Given Information:**

The selling price of product *A* is *B* is *A* and *B* is

**Formula used:**

The partial differentiation of *x* by holding *y* constant as:

The partial differentiate *y* by holding *x* constant as:

**Proof:**

The profit function is given by *R* is the revenue function and *C* is the cost function.

If *x* units are produced of product *A*, each costs *y* units are produced of product *B*, each costs

Thus, the revenue function is

Substitute

Thus, the profit function is

Differentiate *x* by holding *y* constant,

Equate the first derivative of function *x* to zero

Sect-14.1 P-1CPSect-14.1 P-1ESect-14.1 P-2ESect-14.1 P-3ESect-14.1 P-4ESect-14.1 P-5ESect-14.1 P-6ESect-14.1 P-7ESect-14.1 P-8ESect-14.1 P-9E

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