Chapter 10, Problem 10.36P

High-low method and regression analysis. Market Thyme, a cooperative of organic family-owned farms, has recently started a fresh produce club to provide support to the group’s member farms and to promote the benefits of eating organic, locally produced food. Families pay a seasonal membership fee of $100 and place their orders a week in advance for a price of $40 per order. In turn, Market Thyme delivers fresh-picked seasonal local produce to several neighborhood distribution points. Five hundred families joined the club for the first season, but the number of orders varied from week to week.

Tom Diehl has run the produce club for the first season. Tom is now a farmer but remembers a few things about cost analysis from college. In planning for next year, he wants to know how many orders will be needed each week for the club to break even, but first he must estimate the club’s fixed and variable costs. He has collected the following data over the club’s first season of operation:

Week	Number of Orders per Week	Weekly Total Costs
1	415	$26,900
2	435	27,200
3	285	24,700
4	325	25,200
5	450	27,995
6	360	25,900
7	420	27,000
8	460	28,315
9	380	26,425
10	350	25,750

1. 1. Plot the relationship between number of orders per week and weekly total costs.
2. 2. Estimate the cost equation using the high-low method, and draw this line on your graph.
3. 3. Tom uses his computer to calculate the following regression formula:

   $\text{Weekly}\text{total}\text{costs}=\$18,791+(\$19.97\times \text{Number}\text{of}\text{orders}\text{per}\text{weekly})$

Draw the regression line on your graph. Use your graph to evaluate the regression line using the criteria of economic plausibility, goodness of fit, and significance of the independent variable. Is the cost function estimated using the high-low method a close approximation of the cost function estimated using the regression method? Explain briefly.

1. 4. Did Market Thyme break even this season? Remember that each of the families paid a seasonal membership fee of $100.
2. 5. Assume that 500 families join the club next year and that prices and costs do not change. How many orders, on average, must Market Thyme receive each of 10 weeks next season to break even?