Question

Your financial company has two kinds of investment products: P1 and P2. These are sold to...

Your financial company has two kinds of investment products: P1 and P2. These are sold to the public in units where one unit of P1 costs $600 and one unit of P2 costs $400. One can by any non-negative amount of units of P1 or P2.

Each unit of P1 contains 20 shares of Company A, 12 shares of Company B, and 40 shares of Company C. Each unit of P2 contains 30 shares of Company A, 48 shares of Company B, and 20 shares of Company C.

A particular investor states that she requires at least 600 shares of Company A, at least 240 shares of Company B, and at least 800 shares of Company C. How may units of P1 and P2 should the investor purchase so that her requirements above are satisfied and the total cost of her investment products is minimized? What is the least total cost? Provide a complete solution to this linear programming problem. You may assume there actually is a least total cost for the given requirements; you need not verify this.

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Answer #1

Let the no. of units of P1 purchased be "x" and that of P2 be "y".

Thus objective function is = 600x + 400y and this has to be minimized.

Constraints:

1. 20x+30y>=600 (this pertains to the requirement that she requires at least 600 shares of Company A)

2. 12x+48y>=240 (at least 240 shares of Company B)

3. 40x+20y>=800 (at least 800 shares of Company C).

Solving the above in excel, using the solver function, we get the following solution:

Value as computed by solver
Units of P1 15.00
Units of P2 10.00
Formula
Objective function i.e. total cost 13,000.00 600x + 400y
Constraints
600.00 >= 600.00 20x+30y>=600
660.00 >= 240.00 12x+48y>=240
800.00 >= 800.00 40x+20y>=800

So she should buy 15 units of P1 and 10 units of P2 and the least cost is $13,000

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