COMPUTER PROJECT

This project requires a careful and thorough optimization analysis utilizing both
Excel and winplot, as well as manual analytical techniques. You may treat this
as an Indrvrdual project or partner with one other student. In either case you are
not to seek outside assistance( including the Math learning Center) , except
from the instructor.
PROBLEM STATEMENT
During a period, a manufacturer can sell x units of a product
at a price p cents per unit, where,
p = 120 – 0.3x
The cost per unit of making the x units is c cents, where,
c = 4 + 0.1x.
PART I
Be sure to label your work to correspond to the numbers below.
1. (Manual) Formulate the Revenue Function, R(x).
2. (Manual) Formulate the Cost Function, C(x).
3. (Manual) Formulate the Profit Function, P(x)
4. Find the Marginal Revenue Function, MR
5. Find the Marginal Cost Function, MC
Where is the profit zero?
What do you observe on the middle coordinate system when this occurs?
Where is the profit a maximum?
What is the maximum profit?
What do you observe on the middle graph when profit is a maximum?
What do you observe on the lower graph when profit is a maximum?
Where is R > C? (State the range)
What can you say about profit when R > C?
Notice that MR is always decreasing. What does this observation tell you
about the slopes of tangent lines to the revenue function?
Notice that MC is always increasing. What does this observation tell you
about the slopes of tangent lines to the cost function?
Where is MR > 0? (State the range)
What can you say about the Revenue Function (middle coordinate
system) wherever MR > O?
Where is MR < 0? (State the range)
What can you say about the Revenue Function (middle coordinate
system) wherever MR < 0?
Where is MR = 0?
What can you say about the Revenue Function (middle coordinate
system) wherever MR = 0?
Notice that MC > 0 over the entire range of possible interest. What can you
say about the Cost Function (middle coordinate system) wherever MC > 0?
Where is MR > MC? (State the range)
What can you say about the Profit Function (upper coordinate
system) wherever MR > MC?
Where is MR < MC? (State the range)
What can you say about the Profit Function (upper coordinate
system) wherever MR < MC?
Where is MR = MC?
What can you say about the Profit Function (upper coordinate
system) where MR = MC?