Details

Bus 640: Assignment

1. Jennifer Trucking Company operates a large rig transportation business in Texas that transports locally grown vegetables to San Diego, California. The company owns 5 large rigs and hires local drivers paid fixed salaries monthly, regardless of the number of trips or tons of cargo that each driver transports each month. The below table presents details about the number of drivers and the total cargo transported by the company at different staff levels.

Drivers employedTotal Cargo Transported (tons)
15
212
321
432
540
646
751
850

• a. Which inputs are fixed and which are variable in the production function of Jennifer Trucking Company? Over what ranges do there appear to be increasing, constant and/or diminishing returns to the number of drivers employed?
• b.What number of drivers appears to be most efficient in terms of output per driver?
• c.What number of drivers appears to minimize the marginal cost of transportation assuming that all drivers are paid the same salary?

2. The Palms Dry Cleaning Shop in Fort Lauderdale, Florida, faces a highly seasonal demand for its services, as the snow-birds retirees’ flock to Florida in mid-fall to enjoy the mild winter weather and then return to their main homes in mid-spring. Given this seasonality, Palms tries to keep the overhead costs as low as possible and therefore, often uses seasonal contracted labor to man its operations. The following table shows the labor costs in each month of operation over the past 12 months as well as the total number of garments that were dry-cleaned in each month. Palms pay fixed wages per hour to each employee, and we can assume that the costs of other variable inputs (such as chemicals, electricity, etc) have remained constant.

MonthTVC ($)Garments Cleaned
June35,4904,500
July42,4705,575
August48,9806,300
September52,5306,525
October37,4805,325
November33,5104,050
December31,8502,850
January27,8602,450
February22,1601,525
March19,520925
April25,9601,925
May32,9803,500

• a.Derive average variable cost (AVC) data from the data in this table.
• b.Use gradient analysis to provide an estimate of eleven data points that seem to represent the MC curve over this range of outputs. Plot these data points and sketch in estimated MC and AVC curves that seem to best fit these data points.
• c.Suppose that demand is estimated to move from its present (May) level of 3,500 units to 4,000
• d.Assuming that Palm’s price to dry clean a garment has been constant at $15 over the past year, and will remain at that level, what contribution to overheads and profit can it expect in June?

3. Over the past 12 months the Four Winds Novelty Company firm has recorded its internet sales (equals monthly output levels) and its monthly total variable costs (TVC) for a particular novelty item as shown in the following table. Sales have grown over this period with relatively few shocks due to uncontrollable weather, political and sporting events. This online retailer carries no inventories; when it receives a pre-paid on-line order from a customer, it simply buys the product from a supplier and ships it out to the customer.

Sales = OutputTVC ($)
102,813201,953
176,163340,608
196,121377,940
222,885432,863
226,356441,714
296,416629,267
378,446867,596
450,6661,103,807
579,6961,701,125
607,0821,917,861
624,6802,195,352
636,1332,479,195

• a. Using regression analysis, find an equation that best fits the data to represent the TVC function.
• b. At what sales/output level will marginal costs (MC) reach a minimum?
• c. Estimate the value of TVC for sales/output level 250,000 units, and calculate the 95% confidence interval for your estimate.