Question

Product A requires 9 minutes of milling, 7 minutes for inspection, and 6 minutes of drilling per unit; product B requires 10 minutes of milling, 5 minutes for inspection, and 8 minutes of drilling per unit; product C requires 7 minutes of milling, 3 minutes for inspection, and 15 minutes of drilling. The department has 20 hours available during the next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes $2.0 per unit to profit, product B contributes $2.3 per unit, and product C contributes $4.0 per unit. a. How many constraints are there in the Linear Programming Formulation of this problem

Answer 1

The Linear programming problem has 3 constraints :- Milling time, Inspection time, Drilling time constraints.

Explanation:

Product A : 9 minutes milling, 7 minutes inspection, 6 minutes drilling Product B : 10 minutes milling, 5 minutes inspection, 8 minutes drilling Product C : 7 minutes milling, 3 minutes inspection, 15 minutes drilling

Total milling time available = 20 hours = (20 x 60) i.e 1200 minutes Total inspection time available = 15 hours = (15 x 60) i.e 900 minutes Total drilling time available = 24 hours = (24 x 60) i.e 1440 minutes

Let QA, QB, QC be quantities of product A, B, C respectively

• Milling time constraint : 9QA + 10QB + 7QC = 1200
• Inspection time constraint : 7QA + 5QB + 3QC = 900
• Drilling time constraint : 6QA + 8QB + 15QC = 1440