12. Suppose a firm has a production function 10Z = 65 - 2(x - 5)" - 4(y - 4) and the unit prices of the inputs x and y (under pure competition) are 8 and 4, respectively, and the unit price of the output is 32; determine the maximum profit. 13. The relationship between sales S and the amount x and y spent on two advertising media is given by 200 x 100 y S = 5+y 10+ y Net profit is 1/5 of sales minus the costs of advertising. Advertising cost must not exceed the budget set at 25; determine how it should be allocated between the two media in order to maximize net profit. 14. The cost of repairs, C, as a function of the numbers, x and y of inspections at 2 points in a process is given by C = 4x2 + 2y? + 5xy - 20x + 30 To minimize repair costs, what number of inspection should be made at each point if the total number of inspection is at least 10. 15. Find the optimal solution: Max Z = f(x,y,z) = - x2 - 2y2 - 22 + xy + z s.t. xty +z =35 16. Find the optimal solution to the following problem. Minimize f (X1, X2, X3) = x12 + 2x22 + 10x32 s.t. X1 + x22 + x3 - 5 = 0 X1 + 5X2 + X3 - 7 = 0 17. Find the maxima & minima of the following: a) f(x,y) = sinx + siny + sin(xty) OS x S I1/2 0