Fresh Choice, a cooperative of organic family-owned farms outside of Madison, Wisconsin, 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 to the nearby suburban community. Families pay a seasonal membership fee of $75 and place their orders a week in advance for a price of $35 per order. In turn, Fresh Choice delivers fresh-picked seasonal local produce to several neighborhood distribution points. Seven hundred families joined the club for the first season, but the number of orders varied from week to week. Daniel Craig has run the produce club for the first 10-week season. Before becoming a farmer, Daniel had been a business major in college, and he remembers a few things about cost analysis. 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 10 weeks of operation:

Week Number of Orders per Week Weekly Total Costs
1 353 $19,005
2 390 22,605
3 414 22,850
4 450 22,500
5 422 21,950
6 491 24,750
7 449 23,650
8 472 23,005
9 529 25,275
10 508 24,350

Required:

a. Plot the relationship between number of orders per week and weekly total costs.
b. Estimate the cost equation using the high-low method, and draw this line on your graph.
c. Harvey uses his computer to calculate the following regression formula:Total weekly costs = $10,048 + ($28.91 × Number of weekly orders)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.
d. Did Fresh Choice break even this season? Remember that each of the families paid a seasonal membership fee of $75.
e. Assume that 850 families join the club next year and that prices and costs do not change. How many orders, on average, must Fresh Choice receive each week to break even?