The weekly profit P for a widget producer is a function of the number n of widgets sold. The formula is as follows, where P is measured in thousands of dollars, n is measured in thousands of widgets, and the formula is valid up to a level of 12 thousand widgets sold. P = −1 + 2.6n − 0.2n2 Exercise (a) Make a graph of P versus n. Step 1 Because the formula is valid for up to 12 thousand widgets sold, we make the graph using a horizontal span of 0 to . The table of values below led us to choose a vertical span of -2 to 8. The graph is on below. The horizontal axis corresponds to the variable which is thousands of widgets sold, and the vertical axis corresponds to the variable which is weekly profit measured in thousands of dollars. n P 0 -1.00 3.25 5.34 6.50 7.45 9.25 5.94 12.00 1.40 Select the correct graph. Exercise (b) Calculate P(0) and explain in practical terms what your answer means. Exercise (c) At what sales level is the profit as large as possible?
The weekly profit P for a widget producer is a function of the number n of widgets sold. The formula is as follows, where P is measured in thousands of dollars, n is measured in thousands of widgets, and the formula is valid up to a level of 12 thousand widgets sold. P = −1 + 2.6n − 0.2n2 Exercise (a) Make a graph of P versus n. Step 1 Because the formula is valid for up to 12 thousand widgets sold, we make the graph using a horizontal span of 0 to . The table of values below led us to choose a vertical span of -2 to 8. The graph is on below. The horizontal axis corresponds to the variable which is thousands of widgets sold, and the vertical axis corresponds to the variable which is weekly profit measured in thousands of dollars. n P 0 -1.00 3.25 5.34 6.50 7.45 9.25 5.94 12.00 1.40 Select the correct graph. Exercise (b) Calculate P(0) and explain in practical terms what your answer means. Exercise (c) At what sales level is the profit as large as possible?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The weekly profit P for a widget producer is a function of the number n of widgets sold. The formula is as follows, where P is measured in thousands of dollars, n is measured in thousands of widgets, and the formula is valid up to a level of 12 thousand widgets sold.
P = −1 + 2.6n − 0.2n2
Exercise (a)
Make a graph of P versus n.
Step 1
Because the formula is valid for up to 12 thousand widgets sold, we make the graph using a horizontal span of 0 to . The table of values below led us to choose a vertical span of -2 to 8. The graph is on below. The horizontal axis corresponds to the variable
which is thousands of widgets sold, and the vertical axis corresponds to the variable
which is weekly profit measured in thousands of dollars.
Select the correct graph.
| n | P |
| 0 | -1.00 |
| 3.25 | 5.34 |
| 6.50 | 7.45 |
| 9.25 | 5.94 |
| 12.00 | 1.40 |
Select the correct graph.
Exercise (b)
Calculate P(0) and explain in practical terms what your answer means.
Exercise (c)
At what sales level is the profit as large as possible?
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