Originally Posted by

**chiro** Hey RugerWulf.

For this problem you should consider writing your profit equations in terms of hours where you have h1 + h2 = 108 and h3 + h4 = 20 with the equation for the profits being P1 = 35*(3*h1 + 2*h3) and P2 = 20*(2*h2 + 0.5*h4) where total profit is P = P1 + P2 where "profit" is in terms of profit-hours not just profit (different units).

So now you have to maximize P given the constraints. You can get things in terms of just h1 and h3 using the substitution.

Now you have a bivariate function and you can differentiate to find the minimum and maximums of the function taking into account the conditions for the hours.

The standard way to do optimization problems of this type is to use what is known as Lagrange multipliers: have you used them before?