SOLUTION: The weekly profit for a widget producer is a function of the number n of widgets sold. The formula is, P=-2+ 2.9n-0.3n(this exponent is squared, i.e n squared, not sure how to typ

Question 75648This question is from textbook
: The weekly profit for a widget producer is a function of the number n of widgets sold. The formula is, P=-2+ 2.9n-0.3n(this exponent is squared, i.e n squared, not sure how to type it.
Here P is measured in thousands of dollars, n is measured in thousands of widgets, and the formula is valid up to a level of 7 thousand widgets sold.
a)- Make a graph of P verses n.
b)-Calculate P(0) and explain in practical terms what your answer means,
c)At what sales level is the profit as large as possible? This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The weekly profit for a widget producer is a function of the number n of widgets sold. The formula is, P=-2+ 2.9n-0.3n(this exponent is squared, i.e n squared, not sure how to type it.
:
P = -2 + 2.9n - .3n^2
Here P is measured in thousands of dollars, n is measured in thousands of widgets, and the formula is valid up to a level of 7 thousand widgets sold.
a)- Make a graph of P verses n.
:
n = x (horizontal axis), P = y (vertical axis)
plot from x = 0 to x = 7 (max that formula is valid)
:
An example of when x = 2:
y = -2 + 2.9(2) - .3(2^2)
y = -2 + 5.8 - 1.2
y = + 2.6
:
x | y
--------
0 |-2
+1 |+.6
+2 |2.6
+3 |4.0
+4 |4.8
+5 |5.0
+6 |4.6
+7 |3.6
:
your graph should look like this
:

:
b)-Calculate P(0) and explain in practical terms what your answer means,
That means x = 0 (no widgets made), y = -2, A loss of $2000
:
c)At what sales level is the profit as large as possible?
Looking at the graph it's apparent that max profit occurs when 5000 items are
made. A profit of $5000.
:
Did this make sense to you? Any questions?
RELATED QUESTIONS
13. (18 pts) The cost, in dollars, for a company to produce x widgets is given by C(x) (answered by MathLover1)

Help me solve this problem: The profit function for a company is P(x) = 36x^2 + 1875x... (answered by josgarithmetic)

Hi there, I have some of the answers to this following question, but I'm needing help in... (answered by rothauserc)

The Probability of getting a defective Widget is .10 You select five widgets = A.... (answered by Fombitz)

sammy is selling widgets. If he sells 1 widget, it costs him $1 to produce it and he can... (answered by ikleyn)

7. Let q represent the number of widgets sold each week by a store, p represent the... (answered by math_tutor2020)

A company sells widgets. The amount of profit, y, made by the company, is related to the... (answered by ikleyn)

Let q represent the number of widgets sold each week by a store, p represent the price in (answered by greenestamps)

A company has two machines that make widgets. The production costs are listed below. Find (answered by josmiceli)