Eli Safe Ltd produces two products 1 and 2. They are produced on machines A and B, which have annual capacity of 60,000 units and 40,000 units respectively. We will define the number of products made each year as X1 and X2.

Demand for each of the two products is given by the following expressions where P1 and P2 are the prices for product 1 and 2 respectively: X1 = 15,000 – 500P1 X2 = 30,000 – 750P2

The variable production cost per unit for product 1 is $5 and for product 2 is $10.

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a) If Eli Safe’s objective is to maximise unit contribution (price – variable cost per unit), write out an objective function in simplified algebraic form which a expressed only as function of X1 and X2. (12 marks)

b) How would we need to go about solving this problem? (3 marks)

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