4. A vendor makes and sells x strings of beads at her souvenir store every month. The monthly cost and price-demand equations are, respectively, C(x) = 0.00002x3 + 0.04x2 + 150x + 45000 x = 4000 - 200p

a) Given the information above

i. How many sets of beads should she manufacture each month to maximize her revenue?

ii. What is the maximum monthly revenue?

iii. How much should she charge for each set of beads to achieve maximum revenue?

b) Given the information above

i. How many sets of beads should she manufacture each month to maximize her profit?

ii. What is the maximum monthly profit?

iii. How much should the company charge for each set of beads to achieve maximum profit?