After reading the applications section of this chapter (Section 6.10), draw a graph of the mean monthly profit, as a function of the ordered quantity z, and find the value of z that maximizes this profit, in each of the following cases:

(i) ???? = 10, ???? = 5, f (x) = 3x2 8

e−x3∕8, x > 0;

(ii) ???? = 100, ???? = 5, f (x) = 3x2 8

e−x3∕8, x > 0;

(iii) ???? = 10, ???? = 5, f (x) = 1 3 ⋅ 28 x4e−0.5x, x > 0;

(iv) ???? = 100, ???? = 5, f (x) = 1 3 ⋅ 28 x4e−0.5x, x > 0.