A firm has a contract to deliver a certain product to its customer in the future. The amount to be delivered is denoted by Q. The firm collects p dollars for each item from its customers. It has the option of partially or fully cancelling the delivery, in which case it faces a penalty payment of u dollars per cancelled unit. The firm needs to procure the product (or its raw material to produce) from its suppliers. The product costs w dollars now. The firm can procure the item now and keep it in its stocks until delivery. In this case the firm will incur an inventory cost of h dollars per piece. Alternatively, it can wait for the contract execution time and procure it then. However, the wholesale price for the item is uncertain in the future and follows a probability represented by F(x). What is the optimal quantity for the firm to procure now if any?

There are no numbers. it should be shown in terms of variable ( x,y,z,Q, F(x),f(x),p,c,v,etc.)

Answer rating: 100% (QA)

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