linear programming teqniqa

Question

a)      Eddie is buying some tubs for his classroom. Rectangular tub (x) costs $10 each and it requires six square feet of space, and it holds eight cubic feet. Rectangular tub (y) costs $20 each and requires eight square feet of space and it holds twelve cubic feet. He has $140 for this purchase, but he does not have to spend that much. The classroom has room for no more 72 square feet for tubs. How many of each model should he buy in order to maximize storage volume?

Answer 1

3 x tubs, costing $60 and 8 y tubs costing $80

3 x tubs have volume 3(12) = 36, 8 y tubs have volume 8(8) = 64, for total volume = 100 cubic feet

since the tubs come in integer numbers, there are only a few possibilities, about 7

all x tubs, all y tubs, 7y & 0x, 6y& 2x, 5y & 4x, 4y & 6x, 3y & 8x, 2y&5x, 1y&11=0x

try them and all are less volume than 3x &8y tubs, all less than 100