Question

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 1,2,3,4 Fixed Cost to Set Up Production Run 750. 500, 1000, 300 Variable Cost Per Hose 1.25, 1.5, 1, 2 Capacity 6000, 7500, 4000, 5000 (respectively)

a) Define the decision variables

b) Define the objective function

c) Define the constraints

d) Determine an optimal solution

Answer 1

To minimize the total cost of producing 10,000 garden hoses, we need to define decision variables, an objective function, and constraints. Then, we can determine the optimal solution using linear programming techniques.

Step-by-step explanation:

To solve this problem, we need to define the decision variables, objective function, constraints, and determine the optimal solution:

a) Decision variables: Let x1, x2, x3, and x4 represent the number of hoses produced by machines 1, 2, 3, and 4, respectively.

b) Objective function: Minimize the total cost, which is calculated as the sum of the fixed cost and the variable cost per hose multiplied by the number of hoses produced by each machine.

c) Constraints: The total production capacity of each machine must not be exceeded.

d) To determine the optimal solution, we can use linear programming techniques such as the simplex method or graphical method to find the combination of hose production quantities that minimizes the total cost.