Acompany sells many household products through an online catalog. the company needs substantial warehouse space for storing its goods. plans are now being made for leasing warehouse storage space over the next 5 months. just how much space will be required in each of these months is listed in the table below (left). because the space requirements are quite di erent month-to-month, we may choose to lease only the amount needed each month on a month-to-month basis. on the other hand, the monthly cost of leasing space for two or more months at a stretch (in a single lease) is much less than that for multiple one-month leases, so it would be less expensive to have some leases for a longer duration. therefore, it is acceptable to have several leases of varying durations, starting/ending in di erent months, of di erent amounts warehouse space active during any month of the planning horizon. formulate a linear optimization model to the company identify an optimal leasing strategy that meets its needs.

Alocal club is selling christmas trees and deciding how many to stock for the month of december. if demand is normally distributed with a mean of 100 and standard deviation of 20, trees have no salvage value at the end of the month, trees cost $20, and trees sell for $50 what is the service level?

Alandowner entered into a written agreement with a real estate broker whereby the broker would receive a commission of 10% of the sale price if he procured a "ready, willing, and able buyer" for the landowner's property and if the sale actually proceeded through closing. the broker found a buyer who agreed in writing to buy the property from the landowner for $100,000, the landowner's asking price. the buyer put up $6,000 as a down payment. the agreement between the landowner and the buyer contained a liquidated damages clause providing that, if the buyer defaulted by failing to tender the balance due of $94,000 at the closing date, damages would be 10% of the purchase price. the landowner included that clause because she was counting on using the proceeds of the sale for a business venture that would likely net her at least $10,000. the buyer became seriously ill and defaulted. when he recovered, he demanded that the landowner return his $6,000, and the landowner refused. the broker also demanded the $6,000 from the landowner and was refused. the broker and the buyer filed separate suits against the landowner, with the buyer pleading impossibility of performance. the two cases are consolidated into a single case. how should the court rule as to the disposition of the $6,000?

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