Question

Cornell Corporation makes two products, chairs (C) and tables (T). The relationship between profit (PR), the firm’s annual profit (in thousands of dollars), and its output of each good is:

​PR = -80 + 30C + 25T – 4C2 – 3T2 – 2CT

Where C is the firm’s hourly output of chairs and T is the firm’s hourly output of tables. (Neither C nor T needs to be an integer.)

a) Find the output of chairs and the output of tables that will maximize the firm’s profit.

b) What is the maximum profit that the firm can earn per year?

Answer 1

We will solve this problem as a linear programming problem using Excel -> Solver

First setup Excel with details provided.

Now, we will setup Solver table with decision variables, constraints and objective function.

Now, click on Solve the optimal solution.

a)

To maximize profits,

Output of chairs, C = 2.9545

Output of table, T = 3.1818

b)

Maximum profit that firm can earn per year is 4.0909

Please give thumbs up/ likes if you consider my answer useful. Thank you!