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?