Question

A company manufactures two products. If it charges price pi for product i, it can sell qi units of product i, where q1 = 60 - 3p1 + p2 and q2= 80 - 2p2 + p1. It costs $5 to produce a unit of product 1 and $12 to produce a unit of product 2. How many units of each product should the company produce, and what prices should it charge, to maximize its profit?

Answer 1

To maximize its profit, the company needs to determine the quantity and price of each product that will maximize its revenue and minimize its costs. This can be done by finding the profit-maximizing output level, where the marginal revenue equals the marginal cost. By solving the equations for demand and cost, the optimal prices and quantities for each product can be obtained.

Step-by-step explanation:

To maximize its profit, the company needs to determine the quantity and price of each product that will maximize its revenue and minimize its costs. This can be done by finding the profit-maximizing output level, where the marginal revenue equals the marginal cost. The first step is to find the equations for the demand of each product:

q1 = 60 - 3p1 + p2

q2 = 80 - 2p2 + p1

Next, we need to identify the cost of producing each product:

Cost of product 1 = $5 per unit

Cost of product 2 = $12 per unit

After determining the equations for demand and costs, we can equate the marginal revenue with the marginal cost to find the values for p1 and p2 that maximize the profit. By solving the equations, we can obtain the optimal prices and quantities for each product.