The Alphab Group has five divisions A, B, C, D and E. Group management wish to increase
Question:
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.
Required:
(a) Formulate the mathematical model from which the input to the LP programme would be obtained.
(b) Use the linear programme solution in the Appendix in order to answer the following:
(i) State the maximum additional contribution from the expansion strategy and the distribution of the extra capacity between the divisions.
(ii) Explain the cost to the company of providing the minimum 5 per cent increase in capacity at each division.
(iii) Explain the effect on contribution of the limits placed on capacity and investment.
(iv) Explain the sensitivity of the plan to changes in contribution per hour.
(v) Group management decide to relax the 30 000 hours capacity constraint. All other parameters of the model remain unchanged. Determine the change in strategy which will then maximize the increase in group contribution. You should calculate the increase in contribution which this change in strategy will provide.
(vi) Group management wish to decrease the level of investment while leaving all other parameters of the model (as per the Appendix) unchanged.
Determine and quantify the change in strategy which is required indicating the fall in contribution which will occur.
(c) Explain the limitations of the use of linear programming for planning purposes.
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