9. (20 points) Suppose castings cost $800 to produce and each one produced has a probability of .90 of being good (and assume that castings are good/defective independent of one another.) A customer will pay $1400 per casting for 5 good castings. However, the customer will only purchase exactly 5 castings. Assume that defective castings have a salvage value of zero and that your objective is to maximize your expected profit. a. If you are only allowed to start one batch due to time constraints on the order, then it is optimal to start 6 castings. What is the expected profit if you start 6 castings? b. If you could reduce the cost of producing the castings by 10% or increase the revenue per casting sold by 10%, which would you choose? Why? Assume you use a lot size of 6 castings. c. How much would you be willing to pay for a technological improvement that would let you increase the probability of castings being good for this order to 100%? Assume that the technological improvement would only help this one order.9. (20 points) Suppose castings cost $800 to produce and each one produced has a probability of .90 of being good (and assume that castings are good/defective independent of one another.) A customer will pay $1400 per casting for 5 good castings. However, the customer will only purchase exactly 5 castings. Assume that defective castings have a salvage value of zero and that your objective is to maximize your expected profit. a. If you are only allowed to start one batch due to time constraints on the order, then it is optimal to start 6 castings. What is the expected profit if you start 6 castings? b. If you could reduce the cost of producing the castings by 10% or increase the revenue per casting sold by 10%, which would you choose? Why? Assume you use a lot size of 6 castings. c. How much would you be willing to pay for a technological improvement that would let you increase the probability of castings being good for this order to 100%? Assume that the technological improvement would only help this one order