Question

A company makes two calculator models, one designed specifically for financial use and the other designed for scientific use. The financial model contains 10 microcircuits, and the scientific model contains 20. A contract with a supplier of semiconductor chips requires the use of at least 3200 chips each day. A contract with a supplier of the off-on switches used in both calculators requires the use of at least 300 switches each day. The company would like to produce at least 100 financial models each day. If each financial calculator requires 10 production steps and each scientific calculator requires 12 production steps, how many calculators of each type should be produced to minimize the number of production steps

Answer 1

• 280 financial
• 20 scientific

Explanation:

The linear programming problem can be formulated as ...

minimize 10f +12s subject to ...

10f +20s ≥ 3200 . . . . number of chips used

f + s ≥ 300 . . . . . . . . . .number of switches used

f ≥ 100 . . . . . . . . . . . . .minimum number of financial calculators

Graphing these inequalities, we find the feasible region to be bounded by the points (f, s) = (100, 200), (280, 20), (320, 0). The one of these that minimizes the number of production steps is ...

f = 280, s = 20

280 financial and 20 scientific calculators should be produced to minimize the number of production steps.