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Derivatives
|
Price |
Number of Items Sold |
|
|
4.25 |
714495 |
|
|
4.64 |
704405 |
|
|
4.74 |
738689 |
|
|
5.15 |
738423 |
|
|
5.84 |
700775 |
|
|
6.07 |
701370 |
|
|
6.16 |
705884 |
|
|
6.38 |
697011 |
|
|
6.57 |
686771 |
|
|
6.59 |
683839 |
|
|
6.78 |
665641 |
|
|
6.82 |
690920 |
|
|
6.86 |
670827 |
|
|
7.08 |
683833 |
|
|
7.11 |
666674 |
|
|
7.30 |
637978 |
|
|
7.35 |
631497 |
|
|
7.41 |
639231 |
|
|
7.42 |
631739 |
|
|
7.66 |
620396 |
|
|
7.78 |
612080 |
|
|
7.79 |
639209 |
|
|
591471 |
||
|
7.80 |
590248 |
|
|
7.92 |
615265 |
|
|
7.93 |
589644 |
|
|
7.99 |
598021 |
|
|
8.07 |
610704 |
|
|
595432 |
||
|
8.32 |
576894 |
|
|
8.40 |
575995 |
|
|
8.58 |
555844 |
|
|
8.67 |
559958 |
|
|
8.72 |
535670 |
|
|
8.74 |
540079 |
|
|
8.80 |
549971 |
|
|
8.87 |
541065 |
|
|
8.99 |
515531 |
|
|
9.14 |
522314 |
|
|
9.16 |
512325 |
|
|
9.21 |
492818 |
|
|
9.51 |
479736 |
|
|
9.59 |
480402 |
|
|
10.13 |
397314 |
|
|
10.59 |
362052 |
|
|
10.73 |
335221 |
|
|
10.92 |
310495 |
|
|
11.65 |
216427 |
|
|
12.81 |
13666 |
|
|
12.84 |
23702 |
Question 1:
In the table above we have “Price vs. Number of Items Sold”. The first column is the price charged for a point of purchase dog toy in several different markets, while the second column is the number items sold of that item. Plot the data with items sold as the y-variable and determine the quadratic fit to the data. Insert the plot below and write out the quadratic equation allowing you to predict sales as a function of the price charged.
Question 2:
What price would you charge to maximize items sold? (Use the quadratic fit you determined above.)
Question 3:
Write out a quadratic equation which predicts revenue given the price charged. (Use the same procedure as in Question 1.)
Question 4:
What price would you charge to maximize revenue? (Use the quadratic equation from Question 3.)
Question 5:
The cost of manufacturing one of the toys is given by the following equation:
Cost= 800/√Number of items made
Use this function to determine the cost of making the toys in each market for which you have data. Use this cost data to determine the profit you make for each market. Finally, use the profit data to determine what price you should set to maximize profit. (Use the same procedure as in Question 1 and Question 2).
Question 6:
Point out one area where the set up of this homework is unrealistic.
