Question

Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs. Let x 11 = amount shipped from Southern Gas to Hamilton x12 = amount shipped from Southern Gas to Butler x13 = amount shipped from Southern Gas t Clermont x21 = amount shipped from Northwest Gas to Hamilton x22 = amount shipped from Northwest Gas to Butler x23 = amount shipped from Northwest Gas to Clermont

Answer 1

A linear programming model can be used to minimize total distribution costs by determining the amounts shipped from each source to each destination. The objective is to minimize the total distribution costs, which can be formulated as the sum of the costs for each shipment.

Step-by-step explanation:

A linear programming model can be used to determine the plan that will minimize total distribution costs. In this case, the decision variables are the amounts shipped from Southern Gas to each destination (Hamilton, Butler, Clermont) and from Northwest Gas to each destination. Let x11 represent the amount shipped from Southern Gas to Hamilton, x12 represent the amount shipped from Southern Gas to Butler, x13 represent the amount shipped from Southern Gas to Clermont, x21 represent the amount shipped from Northwest Gas to Hamilton, x22 represent the amount shipped from Northwest Gas to Butler, and x23 represent the amount shipped from Northwest Gas to Clermont. The objective is to minimize the total distribution costs, which can be formulated as the sum of the costs for each shipment.