Question

The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good-quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood; each picnic table takes 6 labor hours and 35 feet of redwood. Completed benches will yield a profit of $9 each, and tables will result in a profit of $20 each.

Question 1

The optimal production of benches is ______________ and the optimal production of tables is____________ . (Please only enter an integer and include no units. Hint: Because of the resource constraints, you may not be able to produce 4 tables even if the solution is 3.8; you may have to just produce 3 tables.)

Answer 1

Let x = no. of picnic tables
Let y = no. of benches
:
The labor constraint:
6x + 4y = 1200
4y = 1200 - 6x; divide equation by 4
y = 300 - 1.5x

The material constraint:
35x + 10y = 3500
10y = 3500 - 35x
y = 350 - 3.5x; divide equation by 10

Solving both equations will give us;

0 = -50 - 2x

x = 50/2 = 25

Put the value of x, in material constraint equation:

y = 350 - 3.5(25) = 350 - 87.5 = 262.50, or 262

Hence,

No. of picnic tables = x = 25

No. of benches = y = 262