3. A furniture manufacturer produces tables and chairs using three types of mach
ID: 3137298 • Letter: 3
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.
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
Explanation / Answer
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
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