Business mathematics homework

Part-1

The Milton Lumber Company sells boards of various lengths (4-foot, 7-foot, and 9-foot wood boards). This company’s customers’ demand is 30 for 4-foot boards, 25 for 7-foot boards, and 60 for 9-foot boards per week. Milton Lumber cuts up boards 14 feet long to meet this demand and wants to determine how to satisfy its customers’ needs with minimal waste. First, assume that all boards share the same width and thickness. Then, formulate and solve an IP model.

  • a) Define the decision variables (3 pts)
  • b) Define the objective function (2 pts)
  • c) Define the constraints (2 pts)
  • d) Determine an optimal solution. (3 pts)

 

Part 2:

The Westfall Company is contracted to produce 10,000 garden hoses for a significant discount chain. Westfall has four different machines that can make this kind of hose. Because these machines are from various manufacturers and use different technologies, their specifications are different. Therefore, the company wants to minimize the total cost.

Machine Fixed Cost to Set
Up Production Run		 Variable Cost
Per Hose		 Capacity
1 750 1.25 6000
2 500 1.50 7500
3 1000 1.00 4000
4 300 2.00 5000
  • a) Define the decision variables (2 pt)
  • b) Define the objective function (2 pts)
  • c) Define the constraints (3.5 pts)
  • d) Determine an optimal solution. (2.5 pts)