An electronics firm produces two models of pocket calculators: the A-100 (A), wh

Question

An electronics firm produces two models of pocket calculators: the A-100 (A), which is an inexpensive four-function calculator, and the B-200 (B), which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 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 are optimal weekly profits?

which resource is slack (not fully used)?

Explanation / Answer

The objective of the firm is to maximise Profit, Let X1 be the number of calculators of A-100 AND X2 be the number of calculators of B200

The objective funtion is to maximise

Max Z= X1+4X2 ( Because the profit from A100 is $1 and B 200 is $ 4

Subject to

x1+x2<=2500 ( Two of the calculators can be made a maximum of 2500 units because, maximum cicuit is 2500)

0.25x1+0.5x2<=800 ( Maximum Assembly Hours)

x1<=4000 ( Maximum Sales of A-100)

X2<=1000 ( Maximum Slaes of B-200)

This LPP Question is solved in MS Excel Solver application

The Objective Function 5200 Decision Variable x1 1200 x2 1000 Constraints 2200 2500 Maximum Production Constrainst ( only 2500 circuit) 800 800 Assembly Constrain 1200 4000 Demand for A-100 1000 1000 Demand for B-200 The cicuits are not fully used, there is a slack variable of s1=300

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