Question

You need to buy some filing cabinets. You know that Cabinet X costs $10 per unit, requires six square feet of floor space, and holds eight cubic feet of files. Cabinet Y costs $20 per unit, requires eight square feet of floor space, and holds twelve cubic feet of files. You have been given $140 for this purchase, though you don't 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? Show all your work: set up all inequalities, show your feasible region and your complete analysis.

Answer 1

Answer:

Suppose, the number of cabinet of type X be x and number of cabinets of type Y be y respectively. So, floor space taken by both cabinets = 6x + 8y since, 72 square feet of floor space is available so 6x + 8y lessthanorequalto 72 the total cost of the cabinets = 10x + 20y the available amount of spend is $140. 10x + 20y lessthanorequalto 140 x + 2y plusminus 14 suppose, total storage volume is Z. so, z = 8x + 12y so, the problem is Maximize z = 8x + 12y subject to 6x + 8y lessthanorequalto 72 x + 2y lessthanorequalto 14 x, y greaterthanorequalto 0 graph the equations 6x + 8y = 72 x + 2y = 14 test the point (0, 0) in the inequalities. Inequality 1: 6(0) + 8(0) lessthanorequalto 72 (0) lessthanorequalto 72 inequality 2: (0) + 2(0) lessthanorequalto 14 (0) lessthanorequalto 14 so, the point (0, 0) satisfies both the