Answer:
To minimize the cost, the Chicago plant should run 30 days and the Detroit plant should run 20 days.
Step-by-step explanation:
This is a linear programming question, in which there is a function to optimize (minimize cost) and restrictions, all linear functions.
The objective function is Cost:
C: cost function
H: days of operation for Chicago plant
D: days of operation for Detroit plant
The restrictions are:
- Minimum requirements for radial tires:
- Minimum requirements for standard tires:
- Days are positive integers
We have 3 points in which 2 of the constraints are saturated. In one of this three points is the minimum cost.
We will evaluate them to find the minimum cost:
Point 1: H=0, D=80
Point 2: H=50, D=0
Point 3: H=30, D=20
The third point minimizes the cost.
To minimize the cost, the Chicago plant should run 30 days and the Detroit plant should run 20 days.
