Question

3. A furniture manufacturer produces tables and chairs using three types of machines. The time required to produce the furniture on each machine is given in the follow table:

	Hours required per item
Machine	Table	Chair	Hours available per week
Router	1.5	1.0	1,000
Sander	3.0	4.5	2,000
Polisher	2.5	1.5	1,500

Tables will sell for $350 each and chairs will sell for $125 each. Management has determined that the ratio of chairs to tables produced must be at least 4 to 1.

Management has determined that the ratio of chairs to tables produced must be at least 4 to 1. Write the linear programming formulation to determine how many tables and how many chairs the company should produce.

Answer 1

The question asks only for the formulation of the problem not solution

Variables -

1. No. of chairs to be produced in a week = C

2. No. of tables to be produced in a week = T

Constraints -

1. C and T should be non-negative integers

2. Max available time on router = 1.5T + C <= 1000

3. Max available time on Sander = 3T + 4.5C <= 2000

4. Max available time on polisher = 2.5T + 1.5C <= 1500

5. the ratio of chairs to tables produced must be at least 4 to 1: C >= 4T

Objective

maximize the revenue : 350T + 125C