2. Determine how many months it will be before monthly sales exceed 11,000 units.

to be compounded continuously, then sales must be multiplied by a factor of the form e"t, where r is the monthly sales growth rate (expressed as a decimal) and t is time in months. Use these factors to write each of the following as a function of time t: (a) selling price p per unit (including inflation). (b) number of units x sold per month (including sales I. Inflation Hollingsworth Pharmaceuticals specializes in manufac turing generic medicines. Recently it developed an appe tite suppressant with outstanding profit potential. The new appetite suppressant's total costs, sales, and sales growth, as well as projected inflation, are described as follows. growth). (c) total revenue. (Recall that R-px.) Determine how many months it will be before monthly sales exceed 11,000 units. If you restrict your attention to total costs when x11,000, then after expanding and collecting like terms, C(x) can be written as follows: Total monthly costs, in dollars, to produce x units ( unit is 100 capsules): 2. 0ss 11,000 x 2 11,000 Sales: 10,000 units per month and growing at 1.25% per 15,000 10x 15,000 10x0.001(x - 11,000) C(x) 3. month, compounded continuously Wholesale selling price: $34 per unit C(a) 136,000 12x+0.001x for x11,000 Inflation: Approximately 0.25% per month, compounded Use this form for C(x) with your result from Question 1(b) and with the inflationary factor e25' to express these total costs as a function of time Form the profit function that will be used when continuously, affecting both total costs and selling price Company owners are pleased with the sales growth but are concerned about the projected increase in variable costs when production levels exceed 11,000 units per month. The consensus is that improvements eventually can be made that will reduce costs at higher production levels, thus alter ing the current cost function model. To plan properly for these changes, Hollingsworth Pharmaceuticals would like you to determine when the company's profits will begin to . monthly sales exceed 11,000 units using the total rev enue function from Question 1(c) and the total cost function from Question 3. This profit function should be a function of time t. Find how long it will be before the profit is maximized. You may have to solve P't)-0 by using a graphing calculator or computer to find the t-intercept of the graph of P'() In addition, because P"(t) has large numerical coefficients sides of P'( 0 by 1000 before solving or graphing. 5. decrease. To hel p yo u determine this, answer the following. 1. If inflation is assumed to be compounded continuously, ents, you may want to divide both the selling price and total costs must be multiplied by the factor e02 In addition, if sales growth is assumed