Constraints

• Jan 27th 2009, 02:26 AM
studentme
Constraints
A company manufactures two products, A and B, using two machines I and II. To manufacture a unit of product A requires 6 minutes on Machine I and 5 minutes on Machine II. To manufacture a unit of product B requires 9 minutes on machine I and 4 minutes on machine II. There are 5 hours of machine time available in each work shift on machine I and 3 hours on machine II. The company realises a profit of \$5 on each unit of product A and a profit of \$7 on each unit of product B. The company wishes to determine the combination of products A and B that will yield the most profit. Let x be the number of product A to be produced. Let y be the number of product B to be produced.

The common constraints are x >= 0 and y >= 0

The other constraints are

6x + 9y <= 300 (constraint on machine I time)
5x + 4 y <= 180 (constraint on machine II time)

Can someone explain where the 300 and 180 came from?

Thank you!
• Jan 27th 2009, 04:53 AM
Soroban
Hello, studentme!

Look at the units of time . . .

Quote:

A company manufactures two products, A and B, using two machines I and II.
To make a unit of product A requires 6 minutes on Machine I and 5 minutes on Machine II.
To make a unit of product B requires 9 minutes on machine I and 4 minutes on machine II.

There are 5 hours (300 minutes) of machine time available in each work shift on machine I
and 3 hours (180 minutes) on machine II.