Usine Ltd is a company whose objective is to maximize profits. It manufactures two specialty chemical powders, gamma and delta, using three processes: heating, refining and blending. The powders can be produced and sold in infinitely divisible quantities.
The following are the estimated production hours for each process per kilo of output for each of the two chemical powders during the period 1 June to 31 August:

During the same period, revenues and costs per kilo of output are budgeted as

It is anticipated that the company will be able to sell all it can produce at the above prices, and that at any level of output fixed costs for the three month period will total £36 000.
The company's management accountant is under the impression that there will only be one scarce factor during the budget period, namely blending hours, which cannot exceed a total of 1050 hours during the period 1 June to 31 August. He therefore correctly draws up an optimum production plan on this basis.
However, when the factory manager sees the figures he points out that over the three-month period there will not only be a restriction on blending hours, but in addition the heating and refining hours cannot exceed 1200 and 450 respectively during the three month period.

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Gamma (hours) Delta (hours) Heating Refining Blending 400 100 100 120 90 250 Gamma (E per kilo) Delta (E per kilo) 25000 17000 Selling price Variable costs Contribution 16000 12000 4000