The Alphab Group has five divisions A, B, C, D and E. Group management wish to increase overall group production capacity per year by up to 30 000 hours. Part of the strategy will be to require that the minimum increase at any one division must be equal to 5 per cent of its current capacity. The maximum funds available for the expansion programme are £3 000 000. Additional information relating to each division is as follows:

A linear programme of the plan has been prepared in order to determine the strategy which will maximize additional contribution per annum and to provide additional decision-making information.
The Appendix to this question shows a print-out of the LP model of the situation.
(a) Formulate the mathematical model from which the input to the LP programme would be obtained.

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Existing capacity (hours) Investment cost per hour (E) Average contribution per hour (£) Division 90 20 000 40 000 24 000 50000 12 000 12.50 9.50 14