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? If he forecasts that unused space will be normally distributed with a mean of 15 percent of the contracted amount and a coefficient of variation of 0.6, what is the total space that he should sign contracts for?