Question 2 (modified from Summer 2021 paper)Kamba Ltd. is a supplier of lamps. It purchases one lamp at a cost of €600 and sells it for €750.Kamba uses an annual inventory holding cost of 25% of the purchase price, the cost per orderis €300. Kamba supplies 100 lamps per week to customers.a) Kamba’s inventory problem is to determine the number of lamps to order in anticipation ofcustomer orders and is seeking your advice. Determine the Economic Order Quantity (EOQ)and associated total cost. Show your work.b) A new customer has approached Kamba to propose an exclusive agreement whereby Kambasupplies it, and only it, with 6000 lamps per annum at a price discount of €20 per unit.Should the proposal be accepted? Justify your reasons.c) Suppose the manufacturer determines that weekly demand is, in fact, follows a Normaldistribution with mean 𝜇 = 100 lamps and standard deviation 𝜎 = 24. You may assumethat demand is independent from one week to the next. If the lead time is 5 weeks, what isthe reorder level if the firm is willing to tolerate a 1% chance of a stockout during an ordercycle?Hint: If 𝑋 and Y are independent random variables, with 𝑋~𝑁(µ! , σ!" ) and 𝑌~𝑁4µ# , σ#" 5,then𝑍 = 𝑋 + 𝑌~𝑁4µ! + µ# , σ!" + σ#" 5.

a) The Economic Order Quantity (EOQ) is calculated using the formula:

EOQ = sqrt((2DS)/H)

where: D = Demand rate per year S = Order cost per order H = Holding cost per unit per year

Given that Kamba supplies 100 lamps per week to customers, the annual demand (D) is 100 lamps/week * 52 weeks/year = 5200 lamps/year.

The order cost (S) is €300 per order.

The holding cost (H) is 25% of the purchase price, which is 0.25 * €600 = €150 per lamp per year.

Substituting these values into the EOQ formula gives:

EOQ = sqrt((25200300)/150) = 334 lamps

The total cost associated with this order quantity is the sum of the order cost, holding cost, and purchase cost:

Total Cost = (D/EOQ)*S + (EOQ/2)H + DP

where P is the purchase cost per unit, which is €600.

Substituting the given values into this formula gives:

Total Cost = (5200/334)*300 + (334/2)150 + 5200600 = €3,136,826

b) If Kamba accepts the proposal from the new customer, it will sell 6000 lamps per year at a price of €750 - €20 = €730 per lamp. The total revenue from this sale would be 6000 * €730 = €4,380,000.

However, the total cost associated with this sale would be (6000/334)*300 + (334/2)150 + 6000600 = €3,628,706

Therefore, the profit from this sale would be €4,380,000 - €3,628,706 = €751,294

Since this profit is positive, Kamba should accept the proposal.

c) The reorder level is the demand during the lead time at the desired service level. Given that the weekly demand follows a Normal distribution with mean μ = 100 lamps and standard deviation σ = 24, the demand during the lead time of 5 weeks also follows a Normal distribution with mean 5*μ = 500 lamps and standard deviation sqrt(5)*σ = 53.7 lamps.

If the firm is willing to tolerate a 1% chance of a stockout during an order cycle, the service level is 99%. The z-score associated with this service level is 2.33 (from standard Normal distribution tables).

Therefore, the reorder level is mean + z-score * standard deviation = 500 + 2.33 * 53.7 = 625 lamps.