QUESTION 19 Hot Sauce Company decides to make a special-edition, extra-spicy ver

Question

QUESTION 19 Hot Sauce Company decides to make a special-edition, extra-spicy version of its Really Spicy Hot Sauce. Expected demand for the special-edition version of their hot sauce is estimated to be 3000, normally distributed with a standard deviation of make each bottlo; the bottles are intended to sell for $30. Whatover doesn't sell will bt special-edition hot sauce. How many botties should the company make in order to maximize their expected profit? 2200. It will cost $9.00 to to employees as a gift, thus earning $O in revenuo. takes 3 years for the hot sauce to fully ferment and mature, the Realy Spioy Hot Sauce Company can only make one batch of

Explanation / Answer

Profit per bottle if sold, P = 30-9 = $21

Loss per bottle if unsold, L = $9 ( the production cost)

Therefore, Probability of no loss= P/(P+L) = 21/30 = 0.7 = 70%

From the normal distribution, Z score is determined by Z- inverse of 70% = 0.55

Therefore, Optimal production = estimated demand = Mean + Z* Standard Deviation = 3000 + 0.55 * 2200 = 4210 units

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