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?
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