A small warehouse has 100,000 square feet of capacity. The manager at the wareho

Question

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 a fee of S3 per square foot based on actual usage (and an up-front monthly fee of $200 per customer, but you can simply ignore this). The maintenance cost per square foot of the warehouse is negligible. The warehouse guarantees the contracted space amount even if it has to arrange for extra space at a price of S6 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 with the total space that exceeds the regular capacity of 100,000 square feet. What is the optimal (best) total space size of the contracts he should sign in the following cases: 1. 2. 3. 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. He forecasts that unused space will be uniformly distributed from 10,000 to 30,000 square feet: U[10,000; 30,000] The unused space is forecasted to follow the distribution below: Unused space l 10.000 Probability0.1 | 15.000 | 20,000 | 25,000 | 30,000 0.1 35,000 0.2 0.2 0.3

Explanation / Answer

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 a fee of S3 per square foot based on actual usage (and an up-front monthly fee of $200 per customer, but you can simply ignore this). The maintenance cost per square foot of the warehouse is negligible. The warehouse guarantees the contracted space amount even if it has to arrange for extra space at a price of S6 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 with the total space that exceeds the regular capacity of 100,000 square feet. What is the optimal (best) total space size of the contracts he should sign in the following cases: 1. 2. 3. 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. He forecasts that unused space will be uniformly distributed from 10,000 to 30,000 square feet: U[10,000; 30,000] The unused space is forecasted to follow the distribution below: Unused space l 10.000 Probability0.1 | 15.000 | 20,000 | 25,000 | 30,000 0.1 35,000 0.2 0.2 0.3

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