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Operations Research Models and Methods
Problems Section
Nonlinear Programming Models
 - Nonlinear Variations on a Linear Program

A product is produced at two manufacturing plants and shipped to 3 sales outlets. The unit revenues and the maximum sales at the outlets are shown in the table below.

Sales Outlets




Revenue per unit




Maximum sales

10 units



The data below shows the unit costs and maximum productions at the plants.

Manufacturing Plants



Cost per unit



Maximum production

30 units


The data below shows the shipping costs per unit between plants and sales outlets.

Sales Outlet




Plant I




Plant II




The linear programming model for this situation is shown below.

subject to:

In each of the following three problems we modify the situation in some way. Show the change in the model. When solving with the Solver Add-In of Excel, does one expect that the program will find a global maximum solution or only a local maximum? Justify your conclusion with convexity arguments. The modifications are not cumulative.

a. We can make additional units at the plants above the maximum levels indicated.

b. We discover an odd nonlinear restriction on the amounts of products sold.

c. The amounts of products produced at the two plants must obey the equality constraint:

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Operations Research Models and Methods
by Paul A. Jensen
Copyright 2001 - All rights reserved