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

2

3

4

5

6

7

8

5

12

21

32

40

46

51

50

  1. 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?Fixed variable in the production function of Jennifer Trucking Company – Drivers paid fixed salaries monthly, Nos. of Rigs.Ranges in which there appear to be increasing returns to the number of drivers employed are: from Drivers employed ranging from 1 through 4.
  2.  
  3. Variable varying in the production function of Jennifer Trucking Company – Drivers employed, Total Cargo Transported (tons)
  4. Ans:
Drivers employed Total Cargo Transported TP (tons) Marginal Product Mp= ( TPn- TPn-1)
1

2

3

4

5

6

7

8

5

12

21

32

40

46

51

50

5

7

9

11

8

6

5

1

  1. What number of drivers appears to be most efficient in terms of output per driver?
  2. What number of drivers appears to minimize the marginal cost of transportation assuming that all drivers are paid the same salary?
    1. 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 TVC ($) Garments cleaned
    June

    July

    August

    September

    October

    November

    December

    January

    February

    March

    April

    May

    35,490

    42,470

    48,980

    52,530

    37,480

    33,510

    31,850

    27,860

    22,160

    19,520

    25,960 32,980

    4,500

    5,575

    6,300

    6,525

    5,325

    4,050

    2,850

    2,450

    1,525

    925

    1,925 3,500

     

    1. Derive average variable cost (AVC) data from the data in this table.
    2. 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.
  1. 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?
  2. Ans:
Month Month No. TVC ($) Garments cleaned AVC ($) MC ($)
June 1 35,490 4,500 7.89 7.89
July 2 42,470 5,575 7.62 6.49
August 3 48,980 6,300 7.77 8.98
September 4 52,530 6,525 8.05 15.78
October 5 37,480 5,325 7.04 12.54
November 6 33,510 4,050 8.27 3.11
December 7 31,850 2,850 11.18 1.38
January 8 27,860 2,450 11.37 9.98
February 9 22,160 1,525 14.53 6.16
March 10 19,520 925 21.1 4.40
April 11 25,960 1,925 13.49 6.44
May 12 32,980 3,500 9.42 4.46

Going by the above table, the marginal/incremental cost of increasing the level of units from 3500 units to 4000 units in next month ( June) is 4.46 $ per unit.

So, incremental cost of meeting this demand = $ 2230.

 

  1. 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?Palms tries to keep the overhead costs as low as possible and therefore, often uses seasonal contracted labor to man its operations. Given this data, let’s assume that the overhead cost of the Palm is zero for this problem.
  2. Ans:

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
176,163
196,121
222,885
226,356
296,416
378,446
450,666
579,696
607,082
624,680
636,133
201,953
340,608
377,940
432,863
441,714
629,267
867,596
1,103,807
1,701,125
1,917,861
2,195,352
2,479,195
  1. Using regression analysis, find an equation that best fits the data to represent the TVC function.
  2. At what sales/output level will marginal costs (MC) reach a minimum?

Estimate the value of TVC for sales/output level 250,000 units, and calculate the 95% confidence interval for your estimate.Regression Equation is:y = 3.978 * 250000 – 433467 = $ 561,033 

 

Estimated value of TVC for sales/output level 250,000 units = $ 561,033

y = 3.978x – 433467

    1. Ans:
    Lower 95% Upper 95%
    -711611.7421 -155321.6885
    3.315413164 4.640585786

     

    Lower 95 % interval for my estimate = $ 117241.5487

    Upper 95 % interval for my estimate = $ 1004824.758

     

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Jennifer Trucking Company operates a large rig transportation business in Texas that transports locally grown vegetables Answer