Question

A company needs to purchase several new machines to meet its future production needs. It can purchase three different types of machines A,B,andC. Each machine A costs $80,000 and requires 2,000 square feet of floor space. Each machine B costs$50,000 and requires 3,000 square feet of floor space. Each machine C costs $40,000 and requires 5,000 square feet of floor space. The machines can produce 200, 250 and 350 units per day respectively. The plant can only afford $500,000 for all the machines and has at most 20,000 square feet of room for the machines. The company wants to buy as many machines as possible to maximize daily production.

Let                       Xi= number of machines to be purchased

MAX:                         200X1+250X2+300X3

Subject to:            2X1+3X2+5X3≤20

80X1+50X2+40X3≤500

X1,X2,X3≥0

	A	B	C	D	E	F
1			CapitalExpansion
2
3		MachineTypes
4		Machine1	Machine2	Machine3
5	Numbertobuy					TotalOutput:
6	Machineoutput
7
8	Requirements:				Used	Available
9	Squarefeet
10	Cost

How many of each machine should they purchase?

Answer 1