Project Question :

A pharmaceutical company finds the cost function C for producing a certain antibiotic is:

\[C(x)\] = 0.003 \[{{x}^{2}}\] \[+80x\] + 500,000, where \[C(x)\] is the cost in dollars,

and x is the number of units of the antibiotic, where \[0\le x\le 30,000\] .

The firm sets the selling price at $200 per unit.

1. Express the total revenue R as a function of x .
2. Use Winplot (or some other suitable software) or your calculator to tabulate values of Cost and Revenue for several values of x , say x = 0, 10, 100, 1000, 10,000, etc. Display this in chart form, with the labels of the axes being x , C ( x ) and R ( x ).

1. Use Winplot to graph the cost function C and the revenue function R from part 1

in the same set of axes. Interpret the intersection of the two graphs.

4) What is the break-even-point when cost and revenue are equal?

5) Write an expression for the total profit P as a function of x and use Winplot to

graph the profit function.

1. Find the profit if the company sells 15,000 units.
2. Interpret the graph in terms of profit and loss.

6) Write an explanatory paragraph defining the three functions of cost, revenue and profit.

Use the graphing pattern to develop some conclusions about the profit and loss pattern in this problem.

Price: $9.63

Solution: The downloadable solution consists of 6 pages, 363 words and 4 charts.
Deliverable: Word Document