# A company needs to purchase several new machines to meet

A company needs to purchase several new machines to meet its future production needs. It can purchase three different types of machines A, B, and C. 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 of type i 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 Capital Expansion 2 3 Machine Types 4 Machine 1 Machine 2 Machine 3 5 Number to buy Total Output: 6 Machine output 200 250 350 7 8 Requirements: Used Available 9 Square feet 2,000 3,000 4,000 20,000 10 Cost 80,000 50,000 40,000 500,000

How many of each machine should they purchase?

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