In: Operations Management
Connie Jefferson is the primary flower dealer in her hometown of San Flores. Connie has watched the sales volume of her favorite flower, the yellow rose, change over the past 10 weeks. The changes are due to an experiment that Connie is conducting. She has been told that she could sell more roses by reducing the price, and Connie tends to agree. In her experiment, Connie has set out to determine the relationship between the price charged for yellow roses and the quantity demanded. Over the past 10 weeks, Connie has carefully tracked the selling price of her roses and the quantity sold. Her data are as follows:
Week |
Price |
Quantity Sold |
1 |
$30 |
50 |
2 |
8 |
270 |
3 |
10 |
240 |
4 |
27 |
90 |
5 |
25 |
110 |
6 |
21 |
130 |
7 |
12 |
200 |
8 |
15 |
190 |
9 |
19 |
160 |
10 |
20 |
150 |
a. Develop a least squares regression equation that shows the relationship between the
quantity of roses sold and the price charged.
b. If Connie sets the price at $17, what should be the demand for her roses?
c. Discuss the use of this modeling process in a different business setting.
In this question I will help you find the numerical part.
a. To get the least squares regression regression equation first put the data in excel and insert a scatter plot.
This graph is between price vs. quantity sold.
Now to get the equation make the trendline using layout option in chart tools and select the bottom two check box as shown:
This will give you the required equation on graph.
Thus our least squares regression equation is y = -9.0896x + 328.98
b. If the price is set to $17 we can calculate the demand by putting the value of y=17
17 = -9.0896x+328.98 and solve for x
x = 34.322 = 34 roses