A company needs to purchase several new machines to meet its future production needs. It can purchase three different types of m
achines 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?
