Linear Programming Graphical Solution

Write the program for the following then solve graphically:

You need to buy some filing cabinets. You know that Cabinet X costs ₱1,000 per unit, requires six square feet of floor space, and holds eight cubic feet of files. Cabinet Y costs ₱2, 000 per unit, requires eight square feet of floor space, and holds twelve cubic feet of files. You have been given ₱14,000 for this purchase, though you do not have to spend that much. The office has room for no more than 72 square feet of cabinets. How many of which model should you buy, in order to maximize storage volume?

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Let x = number of model X cabinets purchased

y = number of model Y cabinets purchased

Writing the program for the above problem gives:

O.F. z = 8x + 12y

(This pertains to the volume to be minimized)

Subject to:

1000x + 2000y ≤ 1400

6x + 8y ≤ 72

x ≥ 0

y ≥ 0

The last two constraints are included to see to it that only positive values should form part of the possible solution set.

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