An electronics firm produces two models of pocket calculator

An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week\'s production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each. What is the time constraint?

Solution

This is a simple linear programming problem.

Maximise A+4B

Such that:

A+B<=2500

0.25A+0.5B<=800

A<=4000

B<=1000

A>=0

B>=0

Graphically, this problem becomes:

Time constraint: 0.25A+0.5B<=800

Solution is obtained by substituting corner points and finding the maximum value for profit.

In this case, A=1200, B=1000