Question

x1	p	c
1943	1035	900
3190	581	1130
4570	405	1241
6490	124	1800
7330	85	1620

Price-Demand:

1. Make a scatter plot for p vs x (price-demand plot).
2. Get a regression line that best fits the data in Question 1. You need to type the equation of this line in desmos and graph it with your scatter plot. Please use p(?1) = equation when typing in desmos.
3. Does it look like the regression line models the data well? (Yes or No) Why?
4. Use the equation typed in desmos to find p(0), p(3000), p(6000)
5. What value of x would make p(x) = 0?

Cost:

6. Make a scatter plot for c vs x (total cost plot)
7. Get a regression line that best fits the data in Question 6. You need to type the equation of this line in
8. Does it look like the regression line from Question 7 models the data from Question 6 well? (Yes or No) Why?

8. Use the total cost equation typed in demos to find c(0), c(3000), c(6000)
9. What is the fixed and variable costs from the regression equation you obtained in Question 7?

Revenue

11. Using the regression equation for price-demand from Question 2, determine what the R(x) equation is. Graph this on desmos.
12. Determine the number of units that will maximize the revenue?
13. What is the max revenue?
14. What are the break-even points?
15. What is the number of units that will keep the revenue positive? (Answer in interval notation.)

Profit

16. What is the P(x)? Graph the Profit function on desmos along with the R(x) and c(x).
17. Using the break-even points found in Question 14, what is the profit at these points?
18. For what number of units is the profit positive? (Answer in interval notation.)
19. What number of units will give us the max profit?
20. What is the max profit?

Answer 1

Solution:

PRICE-DEMAND:

(a) The scatter plot is plotted by use of demos,

1500 Price (p) Scatter Plot 1000 500 6000 2000 4000 8000 10000 12000 demand(x1)

(b)

The regression line is obtained by use of data analysis tool of excel, we get the following output. SUMMARY OUTPUT Regression Statistics Multiple R 0.965416 R Square 0.932029 Adjusted R Square 0.909372 Standard Error 116.6751 Observations 5 ANOVA df gnificance F SS MS F Regression 1 559992.7637 559992.8 41.13638 0.00768 Residual 3 40839.23629 13613.08 Total 600832 Coefficients Standard Error P-value Lower 95%Upper 95%ower 95.0pper 95.0% t Stat 1232.853 Intercept 133.3171091 9.247519 0.002676 808.578 1657.127 808.578 1657.127 х1 -0.16725 0.026076999 -6.41376 0.00768 -0.25024 -0.08426 -0.25024 -0.08426

Therefore, the regression line is P(x1) = -0.16725(x1)+1232.85.

(c) Yes, the below graph looks like the regression line model well to the data, since most of the observation lies around the line.

1000 500 8000 10000 6000 4000 2000

(d) The required values are given as below,

We have, p(x1)= -.16725*(x1) +1232.853 p(0) > 1232.853 p(3000)> p(6000) > 731.0973 229.3421 At x1 7371.32, the p(x1) -0 p(7371.32) > 0

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Do post the question again specifying which questions to solve.

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