Question 4 [10 marks Las Vegas supermarket bakery must decide how many wedding c
ID: 353977 • Letter: Q
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Question 4 [10 marks Las Vegas supermarket bakery must decide how many wedding cakes to prepare for the upcoming weekend. Cakes cost $32 each to make, and they sell for S60 each. Unsold cakes are reduced to half-price on Monday, and typically one-third of those are sold. Any that remain are donated toa nearby senior center free. The demand can be a cakes and -- 120 cakes. 1. What inventory model should be used to determine the order quantity to minimize the total expected cost? Why? 2. What is the critical ratio 3. How many wedding cakes should be prepared so as to maximize the total expected profit?Explanation / Answer
Answer 1 - Supermarket should use a single inventory model to determine the order quantity to minimize the total expected cost. A single inventory model focuses on shortage cost and excess cost. The bakery has to strike a balance between these two costs.
Cost of shortage, Cs = Profit lost on one cake = $60-$32 = $ 28
The loss for one cake that is unsold, Cl = Cost of cake - Salvage value = $32 - $32/6 - 0*2/3 = $ 26.66
(Note for above - Suppose you make 10 cakes, you will sell 1/3 cakes for 1/2 value and rest 2/3 for free, Hence for 1 cake , the salvage value = 1/6 of Cost.)
Service level or Critical ratio = Cs / (Cs + Cl) = 28 / 54.66 = 0.51
Meaning, the optimal stocking level must satisfy demand 51 percent of the time. Z-Score for 0.51 = 0.03
Cakes to be made to achieve service level and maximize profit = Mean + Z-score*Standard deviation = 450 + 0.03*120 = 450+3.6 = 454 cakes
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