Thread: maximising profits!!!!!!...help!!!!

• For a firm producing two goods x and y wishes to maximise their profit, as represented by the profit function π = 3x2 – 10xy + 12y2 subject to a production constraint y = 20 – ½ x

(a) find the critical values of x and y at which profit is maximised
(b) find the level of profit obtained

Substitute that value for 'y' into the profit function. This will give you an equation in a single variable and your differential calculus should find the maximum easily.

Or, the geometry of the situation should do it without calculus.

On the third hand, are you SURE you have the problem correctly reported? If so, your solution may be an endpoint that doesn't make much practical sense.