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
|
|
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.