Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Green Thumb, a manufacturer of lawn care equipment, has introduced a new product

ID: 443614 • Letter: G

Question

Green Thumb, a manufacturer of lawn care equipment, has introduced a new product. Each unit costs $150 to manufacture, and the introductory price is $200. At this price, the anticipated demand is normally distributed, with a mean of mu = 100 and a standard deviation of sigma = 40. Any unsold units at the end of the season are unlikely to be valuable and will be disposed of in a post-season sale for $50 each. It costs $20 to hold a unit in inventory for the entire season. How many units should Green Thumb manufacture for sale? What is the expected profit from this policy? On average, how many customers does Green Thumb expect to turn away because of stocking out?

Explanation / Answer

Expected quantity to be sold = 100

Cost of producing each product = $150

Price of each product = $200

Disposal value = $50

Inventory carrying cost = $20

The average demand is 100 with a standard deviation of 40.

Salvage value (s) = $30 ($50-$20)

Cost of understocking = $50 (Price-Cost)

Cost of overstocking = $120 (Cost-salvage value; $150-$30=$120)

Optimal cycle service level = 0.2941 (Price-Cost)/Price-Salvage Value)

i.e., Optimal cycle service level = ($200-$150)/$200-$30) = 50/170= 0.2941

Optimal lot size = 78.34 [F-1(CSL, Mean, SD)]

Expected Profit = $2657