BUS640 Week 3 Assignment

Production Cost Analysis and Estimation Applied Problems
Please, complete the following 3 applied problems in a Word or Excel document. Show all your
calculations and explain your results. Submit your assignment in the drop box by using the
Assignment Submission button.
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 employed
Total Cargo Transported (tons)
1
5
2
12
3
21
4
32
5
40
6
46
7
51
8
50
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?
1. 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 pays 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.
Month
June
July
August
September
October

TVC ($)
35,490
42,470
48,980
52,530
37,480

Garments cleaned
4,500
5,575
6,300
6,525
5,325

November
December
January
February
March
April
May

33,510
31,850
27,860
22,160
19,520
25,960

4,050
2,850
2,450
1,525
925
1,925

32,980

3,500

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 units next month (June). What is the incremental cost of meeting this
demand?
d. Assuming that Palm’s price to dry clean a garment has been constant at $15 over the
past year, and will remain at that level, what contribution to overheads and profit can
it expect in June?
2. 3. Over the past 12 months the Four Winds Novelty Company firm has recorded its internet sales
(equals monthly output levels) and its monthly total variable costs (TVC) for a particular novelty
item as shown in the following table. Sales have grown over this period with relatively few
shocks due to uncontrollable weather, political and sporting events. This online retailer carries no
inventories; when it receives a pre-paid on-line order from a customer, it simply buys the product
from a supplier and ships it out to the customer.
Sales = Output
TVC ($)
102,813

201,953

176,163

340,608

196,121

377,940

222,885

432,863

226,356

441,714

296,416

629,267

378,446

867,596

450,666

1,103,807

579,696

1,701,125

607,082

1,917,861

624,680

2,195,352

636,133

2,479,195

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.