The quantity, Q, of a good produced depends on the quantities x1 and x2 of the two main materials used: 0.5 0.5 Q=x1 x2 . Material x1 costs $60 per unit, and material x2 costs $65 per unit. We want to minimize the cost of producing 100 units of the good. Using Lagrange multipliers, we see that the minimum cost of $ I occurs when x1 = a and x2 =