PLEASE SHOW DETAILED SOLUTION PROCEDURES

Problem 1:

A small warehouse has 100,000 square feet of capacity. The manager at the warehouse is in the process of signing contracts for storage space with customers. The contract has an upfront monthly fee of $200 per customer and then a fee of $3 per square foot based on actual usage. The warehouse guarantees the contracted amount even if it has to arrange for extra space at a price of $6 per square foot. The manager believes that customers are unlikely to use the full contracted amount at all times. Thus, he is thinking of signing contracts that exceed 100,000 square feet. He forecasts that unused space will be normally distributed, with a mean of 20,000 square feet and a standard deviation of 10,000 square feet. What is the total size of the contracts he should sign

(Solution: 20,000)

Problem 2:

A department store has purchased 5,000 swimsuits to be sold during the summer sales season. The season lasts three months, and the store manager forecasts that customers buying early in the season are likely to be less price sensitive and those buying later in the season are likely to be more price sensitive. The demand curves in each of the three months are forecasted to be as follows:

D1=2,000 10p1

D2=2,000 20p2

D3=2,000 30p3

(a) If the department store is to charge a fixed price over the entire season, what should it be? What is the resulting revenue?

(b) If the department store wants dynamic prices that vary by month, what should they be? How does this affect profits relative to charging fixed prices?

(c) If each swimsuit costs $40 and the store plans to charge dynamic prices, how many swimsuits should it purchase at the beginning of the season?

-Use Excel Solver to get solutions

-Please list the objective function and the constraints for each decision model

Fixed price model:

Solution: p = $50 and total revenue of $150,000

Dynamic price model:

Solution: p1 = $100, p2 = $50, p3 = $33.33 and the total revenue is $183,333.

Quantity model:

Solution: q = 1,800, p1= $120, p2= $70, p3= $53.33 and the total profit is $87,333.

Note that if each unit costs $40, the profit in this case is higher than starting with 5,000 units (which results in a loss with either fixed or dynamic pricing).