A foundry receives an order for specialty castings. Cost of producing each casting is estimated to be $15,000. The customer requires that exactly 4 good castings be supplied. The customer will pay $20,000 for each good casting. If fewer than four good castings are available, none will be purchased. Each casting is produced independently and the probability of an individual casting being acceptable to the customer is .80. 1/ Develop the expected profit function to be maximized? 2/ Determine the production lot size that maximizes expected profit? 3/ Determine the lot size that will yield a probability of .90 of producing at least 4 good castings. What is the expected profit for the lot size obtained?