Problema Solution
An office manager wants to buy filing cabinets. Cabinet X costs $100, requires 6 square feet of floor space, and holds 8 cubic feet. Cabinet Y costs $200, requires 8 square feet of floor space, and holds 12 cubic feet. No more than $1400 can be spent, and the office has room for no more than 72 square feet of cabinets. The office manager wants the maximum storage capacity within the limits imposed by funds and space. How many of each type of cabinet should be bought?
Answer provided by our tutors
Cabinet X = $100
Cabinet X = Area = 6, V = 8
Cabinet Y - $200
Cabinet Y : A = 8, V = 12
Total A = 72
Total cost = 1400
Find maximum storage capacity
Two equations, two unknowns
100X + 200Y = 1400 (1)
6X + 8Y = 72 (2)
Substitute Equation (1):
X = 12 - (4/3)Y
100(12-(4/3)Y) + 200Y = 1400 (1)
Solve for Y
Y = 3 cabinets
X = 8 cabinets