Higgins Co (HC) manufactures and sells pool cues and snooker cues. The cues both use the same

Question:

Higgins Co (HC) manufactures and sells pool cues and snooker cues. The cues both use the same type of good quality wood (ash) which can be difficult to source in sufficient quantity. The supply of ash is restricted to 5 400 kg per period. Ash costs $$40$ per kg.

The cues are made by skilled craftsmen (highly skilled labour) who are well known for their workmanship. The skilled craftsmen take years to train and are difficult to recruit. HC’s craftsmen are generally only able to work for 12 000 hours in a period. The craftsmen are paid $$18$ per hour.

HC sells the cues to a large market. Demand for the cues is strong, and in any period, up to 15 000 pool cues and 12 000 snooker cues could be sold. The selling price for pool cues is $$41$ and the selling price for snooker cues is \($69.

Manufacturing\) details for the two products are as follows:

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HC does not keep inventory.
Required:

(a) Calculate the contribution earned from each cue.

(b) Determine the optimal production plan for a typical period assuming that HC is seeking to maximise the contribution earned. You should use a linear programming graph (using the graph paper provided), identify the feasible region and the optimal point and accurately calculate the maximum contribution that could be earned using whichever equations you need.
Some of the craftsmen have offered to work overtime, provided that they are paid double time for the extra hours over the contracted 12 000 hours. HC has estimated that up to 1 200 hours per period could be gained in this way.
Required:

(a) Explain the meaning of a shadow price (dual price) and calculate the shadow price of both the labour (craftsmen) and the materials (ash).

(b) Advise HC whether to accept the craftsmens’ initial offer of working overtime, discussing the rate of pay requested, the quantity of hours and one other factor that HC should consider.