A manufacturer can produce at most 140 units of a certain product each year. The demand equation for the product is pequalsq squared minus 100 q plus 4800 and the manufacturer's average-cost function is c overbarequalstwo thirds q squared minus 30 q plus StartFraction 15 comma 000 Over q EndFraction . Determine the profit-maximizing output q and the corresponding maximum profit.

Fanning company is considering the addition of a new product to its cosmetics line. the company has three distinctly different options: a skin cream, a bath oil, or a hair coloring gel. relevant information and budgeted annual income statements for each of the products follow. skin cream bath oil color gel budgeted sales in units (a) 110,000 190,000 70,000 expected sales price (b) $8 $4 $11 variable costs per unit (c) $2 $2 $7 income statements sales revenue (a × b) $880,000 $760,000 $770,000 variable costs (a × c) (220,000) (380,000) (490,000) contribution margin 660,000 380,000 280,000 fixed costs (432,000) (240,000) (76,000) net income $228,000 $140,000 $204,000 required: (a) determine the margin of safety as a percentage for each product. (b) prepare revised income statements for each product, assuming a 20 percent increase in the budgeted sales volume. (c) for each product, determine the percentage change in net income that results from the 20 percent increase in sales. (d) assuming that management is pessimistic and risk averse, which product should the company add to its cosmetics line? (e) assuming that management is optimistic and risk aggressive, which product should the company add to its cosmetics line?