Question

5. You are the assistant manager of an appliance store. Next month you will order two types of stereo systems. How many of each model should you order to minimize the cost? Model A: Your cost if $300. Your profit is $40. Model B: Your cost is $400. Your profit is $60. You expect a profit of at least $4800. You expect to sell at least 100 units.

Answer 1

Let x units of model A and y units of model B is ordered.

Then from the given condition we must have selling atleast 100 units.

So x+y ≥100 ... i

Next is to maximise profit. Profit is 40 for A and 60 for B.

40x+60y is the total profit

From the condition profit ≥4800

i.e. 40x+60y≥4800

Divide by 20 to get

2x+3y≥240 ... ii

The objective function is Cost function

Z = 300x+400y and to minimize Z

Solving constraints we get 2x+3y≥240 and

2x+2y≥200

y≥40 and x≥60.

So possibilities are (120,0) (0,100) or (40,60)

Let us calculate Z for each of these points.

Z(120,0) = 36000

z(0.100) = 40000

Z(60,40) = 18000+16000 = 34000

Since cost is minimum for (60,40)

60 units of model A and 40 units of model B should be ordered.