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Question: A firm manufactures products A and B using the two inputs X and Y in the following quantities:

1 tonne of A requires 80 units of X plus 148 units of Y

1 tonne of B requires 200 units of X plus 120 units of Y

The profit per unit of A is £20, and the per-unit profit of B is £30. If the firm has at its disposal 1,600 units of X and 1,800 units of Y, what combination of A and B should it manufacture in order to maximize profit? (Fractions of a tonne may be produced.)

Should the firm change its production mix if per-unit profits alter to

(a) £25 each for both A and B, or

(b) £30 for A and £20 for B?

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