18. A furniture company manufactures four models of desks. Each desk is first constructed in the carpentry shop and is next sent to the finishing shop, where it is varnished, waxed and polished. The number of man-hours oflabour required in each shop is as follows:

Because oflimitations in capacity of the plant, no more than 6,000 man-hours can be expected in the carpentry shop and 4,000 in the finishing shop in the next six months.
The profit (revenue minus labour costs) from the sale of each desk is as follows:

Assuming that raw materials and supplies are available in adequate quantities and all desks produced can be sold, set the linear programme of the problem of the company in terms of maximum profit and determine the optimal mix which will maximise profit.

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Desk I Desk II Desk III Desk IV Carpentry shop Finishing shop 4 9 7 10 1 1 3 40