Question

The Knitting Company, TKC, is planning production for its four styles of sweaters that are popular during Christmas. All styles have normally distributed demand. The best-selling style has a demand of 30,000 and a standard deviation of 5,000. The other styles have a demand of 10,000 with a standard deviation of 4,000. Production cost is $20 and units are sold for a wholesale price of $35. Unsold units are sold at the end of the season for $15. It costs $2 to hold the units in inventory for the entire season if they do not sell. How many sweaters of each type should TKC manufacture?

Answer 1

To determine the profit-maximizing quantity, calculate total revenue, marginal revenue, total cost, and marginal cost for each output level. The profit-maximizing quantity is 2 units, resulting in the highest difference between total revenue and total cost. If the cost of labor rises to $200/unit, the profit-maximizing quantity would be 3 units.

Step-by-step explanation:

To determine the profit-maximizing quantity, we need to calculate the total revenue, marginal revenue, total cost, and marginal cost for each output level. Here's the table: Output LevelTotal RevenueMarginal RevenueTotal CostMarginal Cost1727216410021447224884321672362114428872546184536072816270

From the table, we can see that the profit-maximizing quantity is 2 units as it results in the highest difference between total revenue and total cost ($144 - $248 = -$104). At this quantity, the marginal revenue ($72) is still greater than the marginal cost ($84), resulting in a negative profit. If the cost of labor rises to $200/unit, the profit-maximizing quantity would be 3 units ($216 - $362 = -$146), as it would result in the highest difference between total revenue and total cost.