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3. 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 =100 and a standard deviation of =40. Any unsold units at the end of the season will be sold at post=season sale for $50 each. It costs $20 to hold a unit in inventory for the entire season. (15 points total) a. How many units should Green Thumb manufacture for sale? (5 points) b. What is the expected profit from this policy? (5 points) c. On average, how many customers does Green Thumb expect to turn away because of stocking out? (5 points

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sakhilemdletshesm

Answer:

Expected profit = $2657

Explanation:

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

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jayilych4real

The expected profit from this policy is:

  • $2657

What is Expected Profit?

This refers to the certain probability which is calculated of a certain profit can be gotten, multiplied by the cost.

Hence, our parameters are:

  • Expected quantity to be sold = 100
  • Cost of producing each product = $150
  • Price of each product = $200
  • Disposal value = $50
  • Inventory carrying cost = $20

Therefore, the average demand =100 with a standard deviation = 40.

Next, we find the 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)

Then, we find the optimal lot size = 78.34 [F-1(CSL, Mean, SD)]

Expected Profit = $2657

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