Question

Cindy's clothing store sells raincoats. The monthly demand for raincoats is normally distributed, with an average of 20 raincoats and a standard deviation of 5 rain coats. Cindy's supplier of raincoats charges a $90 processing fee per shipment of raincoats. After Cindy places an order to her supplier, it takes 3 weeks for the raincoats to arrive to the clothing store. Furthermore, Cindy must provide occasional maintenance to maintain the quality of the raincoats. Cindy pays an average of $12 in maintenance fees per raincoat per year

a)What is the optimal order quantity that Cindy should make to her supplier?

b) Assume Cindy currently sets her reorder point at 16 raincoats. What is the service level corresponding to this reorder point?

c) Assume Cindy wants to provide a 94% service level. What should Cindy set as her reorder point?

d) What is the safety stock corresponding to a 90% service level?

Answer 1

The profit-maximizing quantity for Doggies Paradise Inc. can be found by analyzing the marginal cost and marginal revenue. Calculating total revenue, marginal revenue, total cost, and marginal cost for each output level allows for this determination. The optimal quantity is where marginal cost equals marginal revenue.

Step-by-step explanation:

The problem presented involves a perfectly competitive firm, Doggies Paradise Inc., selling dog coats and seeking to maximize profits. To solve this problem, we can use cost and revenue data to calculate total revenue, marginal revenue, total cost, and marginal cost at different production levels. The profit-maximizing quantity is the output level where marginal cost equals marginal revenue (MC=MR). Below is a table with the calculated values:

• Total Revenue (TR): TR = Price x Quantity
• Marginal Revenue (MR): MR = Change in TR / Change in Quantity
• Total Cost (TC): TC = Fixed Costs + Variable Costs
• Marginal Cost (MC): MC = Change in TC / Change in Quantity

We can then plot these values on graphs to visually determine the profit-maximizing output level. A total revenue and total cost curves graph will cross at the profit-maximizing point if it exists (where total revenue exceeds total cost by the greatest amount). The marginal revenue and marginal cost curves graph will intersect at the profit-maximizing output as well.