There are multiple questions here. I tried asking them individually, but they each rely on the prior question to solve.

Scenario 1:Hollingsworth Pharmaceuticals specializes in manufacturing generic medicines. Recently it developed an appetite 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.

Total monthly costs:in dollars, to producexunits (1 unit is 100 capsules):

C(x) = 15,000+10x. 0x11,000

C(x) =15,000 + 10x+ 0.001(x11,000)^2 x11,000

C(X) is both of these....

Sales:10,000 units per month and growing at 1.25% per month, compounded continuouslyWholesale selling price:$34 per unit

Inflation:Approximately 0.25% per month, compounded 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 altering 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 decrease. To help you determine this, answer the following.

1. If inflation is assumed to be compounded continuously, the selling price and total costs must be multiplied by the factore0.0025t. In addition, if sales growth is assumed to be compounded continuously, then sales must be multiplied by a factor of the formert, whereris the monthly sales growth rate (expressed as a decimal) andtis time in months. Use these factors to write each of the following as a function of timet:

(a) selling pricepper unit (including inflation).

(b) number of unitsxsold per month (including sales growth).

(c) total revenue. (Recall thatR=px.)

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

3. If you restrict your attention to total costs whenx$ 11,000, then after expanding and collecting like terms,C(x) can be written as follows:

C(x)=136,00012x+0.001x^2 for x 11,000

Use this form forC(x) with your result from Question 1(b) and with the inflationary factor

e^0.0025tto express these total costs as a function of time.

4. Form the profit function that will be used when monthly sales exceed 11,000 units using the total revenue function from Question 1(c) and the total cost function from Question 3. This profit function should be a function of timet.

5. Find how long it will be before the profit is maximized. You may have to solveP(t) = 0 by using a graphing calculator or computer to find thet-intercept of the graph ofP(t). In addition, becauseP(t) has large numerical coefficients, you may want to divide both sides ofP(t) = 0 by 1000 before solving or graphing.