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Model Building in Mathematical Programming, 5th Edition by H. Paul Williams

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Chapter 14

Solutions to problems

Optimal solutions to the problems presented in Part II are given here. The main purpose in giving the solutions is to allow the reader to check solutions he/she may have obtained to the same problems. All the solutions given here result from the formulations presented in Part III. Sometimes, alternative optimal solutions are possible, as described in Section 6.2, although the optimal value of the objective function will be unique.

If the reader obtains a different solution to a problem from that given here, he/she should attempt to validate his/her solution using the principles described in Section 6.1. In many cases, it is realistic to take the solution given here to represent the current operating pattern in the situation being modelled. The different solution obtained can then be validated relative to this solution.

14.1 Food manufacture 1

The optimal policy is given in Table 14.1.

Table 14.1

c14-tab-0001

The profit (income from sales − cost of raw oils) derived from this policy is £107 843. This figure includes storage costs for the last month.

There are alternative optimal solutions.

14.2 Food manufacture 2

This model proved comparatively hard to solve. The optimal solution found is given in Table 14.2.

Table 14.2

c14-tab-0002

The profit (income from sales − cost ...

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