Question 2: (13 points)A manufacturer of greeting cards must determine the order size of a certain popular line of cards. Call it line A. The demand for these cards has been a fairly steady 500 per week. The manufacturer is currently using an order size of 10,000. The order cost is $5,200 each time an order is placed. Assume that for each card the cost is $6.40. The accounting department of the firm has established an interest rate to represent the opportunity cost of alternative investment and storage costs at 25 percent of the value of each card.a.(4 points) What is the optimal value of the EOQ for line A of greeting cards? Assume only one line of cards is carried.b.(4 points) Determine the additional annual cost resulting from using the wrong order size. Assume only one line of cards is carried.c.(5 points) Continues from part a. Suppose that there is another inexpensive line of cards, line B. The demand for line B is 52,000 per year. The order cost is $260 per order. Cost of each card is $2.56. Holding cost is 25%. However, lines A and B share the same storage space of 299 square feet. Each square foot holds 50 cards of each line. Compute the optimal order sizes of lines A and B. Show one trial with Lagrange multiplier .gif”>.Question 3: (12 points)Suppose that item A has a unit cost of $4, a production setup cost of $540, and a monthly demand of 450 units. It is estimated that the cost of capital is approximately 15 percent per year. Annual storage cost amounts to 3 percent and breakage to 2 percent of the value of the each item. Assume that item A has a production rate of 7,200 items per year.a.(2 points) Compute EPQ of item A.b.(3 points) What is the percentage of downtime in each cycle if only item A is produced? Compute cycle time and downtime. Express downtime as a percentage of cycle time.c.(4 points) What is the cycle time if both items A and B are produced in a single facility? Assume negligible setup times for both items A and B.d.(3 points) Continues from part c. What is the percentage of idle time in each cycle?Question 4: (10 points)One of the products stocked at Weisss paint store is a certain type of highly volatile paint thinner that, due to chemical changes in the product, has a shelf life of exactly one year. Al Weiss purchases the paint thinner for $32 a can and sells it for $60 a can. The supplier buys back cans not sold during the year for $20 for reprocessing. The demand for this thinner generally varies from 50 to 100 cans a year.a.Assuming that all values of the demand from 50 to 100 are equally likely, what is the optimal number of cans of paint thinner for Al to buy each year?b.More accurate analysis of the demand shows that a normal distribution gives a better fit of the data. The distribution mean is identical to that used in part a, and the standard deviation estimator turns out to be 12. What policy do you now obtain?Question 5: (10 points)Assume that weekly demand for cookies is as follows:Demand Probability of Demand1,600 dozen 0.051,700 0.101,800 0.151,900 0.202,000 0.252,100 0.102,200 0.102,300 0.05Selling price is $3/dozen and purchase price is $2/dozen. The cookies are made in the beginning of each week and all cookies unsold by the end of the week are sold at a reduced price of $0.75/dozen. What is the optimal number of cookies to make?Question 6: (10 points)The home appliance department of a large department store is using a lot size-reorder point system to control the replenishment of a particular model of FM table radio. The store sells an average of 7200 radios each year. Annual demand follows a normal distribution with standard deviation 200. The store pays $25 for each radio, which it sells for $110. Fixed cost of replenishment amounts to $50. The accounting department recommends a 20 percent interest rate for the cost of capital. Storage costs amount to 3 percent and breakage to 2 percent of the value of each item. If a customer demands the radio when it is out of stock, the customer will generally go elsewhere. Loss-of-goodwill costs are estimated to be about $20 per radio. Replenishment lead-time is three months. Consider .gif”>a.(2 points) What is the expected average inventory?b.(1 point) What is the expected annual holding cost (regular and safety stock)?c.(2 points) What is the probability of stockout during lead time? (Remember to state answer in four decimal places)d.(1 point) What is the expected annual number of orders?e.(1 point) What is the stockout cost per unit?f.(2 points) What is the expected number of units stockout in each cycle?g.(1 point) What is the fill rate? (Remember to state answer in four decimal places)Question 2: (13 points)A manufacturer of greeting cards must determine the order size of a certain popular line of cards. Call it line A. The demand for these cards has been a fairly steady 500 per week. The manufacturer is currently using an order size of 10,000. The order cost is $5,200 each time an order is placed. Assume that for each card the cost is $6.40. The accounting department of the firm has established an interest rate to represent the opportunity cost of alternative investment and storage costs at 25 percent of the value of each card.a.(4 points) What is the optimal value of the EOQ for line A of greeting cards? Assume only one line of cards is carried.b.(4 points) Determine the additional annual cost resulting from using the wrong order size. Assume only one line of cards is carried.c.(5 points) Continues from part a. Suppose that there is another inexpensive line of cards, line B. The demand for line B is 52,000 per year. The order cost is $260 per order. Cost of each card is $2.56. Holding cost is 25%. However, lines A and B share the same storage space of 299 square feet. Each square foot holds 50 cards of each line. Compute the optimal order sizes of lines A and B. Show one trial with Lagrange multiplier .gif”>.Question 3: (12 points)Suppose that item A has a unit cost of $4, a production setup cost of $540, and a monthly demand of 450 units. It is estimated that the cost of capital is approximately 15 percent per year. Annual storage cost amounts to 3 percent and breakage to 2 percent of the value of the each item. Assume that item A has a production rate of 7,200 items per year.a.(2 points) Compute EPQ of item A.b.(3 points) What is the percentage of downtime in each cycle if only item A is produced? Compute cycle time and downtime. Express downtime as a percentage of cycle time.c.(4 points) What is the cycle time if both items A and B are produced in a single facility? Assume negligible setup times for both items A and B.d.(3 points) Continues from part c. What is the percentage of idle time in each cycle?Question 4: (10 points)One of the products stocked at Weisss paint store is a certain type of highly volatile paint thinner that, due to chemical changes in the product, has a shelf life of exactly one year. Al Weiss purchases the paint thinner for $32 a can and sells it for $60 a can. The supplier buys back cans not sold during the year for $20 for reprocessing. The demand for this thinner generally varies from 50 to 100 cans a year.a.Assuming that all values of the demand from 50 to 100 are equally likely, what is the optimal number of cans of paint thinner for Al to buy each year?b.More accurate analysis of the demand shows that a normal distribution gives a better fit of the data. The distribution mean is identical to that used in part a, and the standard deviation estimator turns out to be 12. What policy do you now obtain?Question 5: (10 points)Assume that weekly demand for cookies is as follows:Demand Probability of Demand1,600 dozen 0.051,700 0.101,800 0.151,900 0.202,000 0.252,100 0.102,200 0.102,300 0.05Selling price is $3/dozen and purchase price is $2/dozen. The cookies are made in the beginning of each week and all cookies unsold by the end of the week are sold at a reduced price of $0.75/dozen. What is the optimal number of cookies to make?Question 6: (10 points)The home appliance department of a large department store is using a lot size-reorder point system to control the replenishment of a particular model of FM table radio. The store sells an average of 7200 radios each year. Annual demand follows a normal distribution with standard deviation 200. The store pays $25 for each radio, which it sells for $110. Fixed cost of replenishment amounts to $50. The accounting department recommends a 20 percent interest rate for the cost of capital. Storage costs amount to 3 percent and breakage to 2 percent of the value of each item. If a customer demands the radio when it is out of stock, the customer will generally go elsewhere. Loss-of-goodwill costs are estimated to be about $20 per radio. Replenishment lead-time is three months. Consider .gif”>a.(2 points) What is the expected average inventory?b.(1 point) What is the expected annual holding cost (regular and safety stock)?c.(2 points) What is the probability of stockout during lead time? (Remember to state answer in four decimal places)d.(1 point) What is the expected annual number of orders?e.(1 point) What is the stockout cost per unit?f.(2 points) What is the expected number of units stockout in each cycle?g.(1 point) What is the fill rate? (Remember to state answer in four decimal places)