Buttercup Ltd manufactures and sells 3 products (R, S and T). These products are made using the same machinery. The total machining time available each month is 10,500 hours but this is insufficient to produce all the units of R, S and T required to meet maximum demands. No stocks of these products are held.

The following information is available: Product R   Product S  Product T

Selling price per unit $  60 $ 75 $ 84

Contribution to sales ratio 20% 24% 25%

Machining minutes per unit 40 54 75

Maximum monthly demand (units) 9,000 6,000 3,000

Required:

(a) Calculate the monthly shortfall in machining hours.

(b) Determine the monthly production plan in units that will maximise the company's total contribution.