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?