game held at Midwest Arena at Milwaukee. I am determined to make some money dist
ID: 3059965 • Letter: G
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game held at Midwest Arena at Milwaukee. I am determined to make some money distributed between these). I can buy the beer at $2 a bottle and sell $5 a bottle. Ifi bad, and I would like to consider its monetary value amounts to S0.2 per bottle 4. (20 pts) Today is a good day. UWM basket ball team is at the NCAA championship e of beer, my tnends will laugh at me, which will make me ieel (consider this as loss of goodwill by customers). If I have any leftovers when the is over, I will drink it all, in which case, it is worth S0.5 a bottle to me,. How many bottles should I buy to maximize my expected profit (including bad (by being laughed at) and good (by drinking a lot of beer)? hs 1h45) erche:. A company has the option of purchasing a good or manufacturing the item. If the item p, units per year It D 20, determine r is purchased, the the ged $25 per unit plus a cost of $6 per order, If 3 to sct up a production run, and annual demand is 3,000 units per year, the Ks 25 manufactures the item, it has a production rate of 8,000 units annuarholdingcosti. T09aandthecostorman whether the company should purchase or manufacture the item. Purchase : 2.16 1 199.56 Ic(71: 3354.233S4+1199.96 909.2 is the od chace beense the c by is les ten the cet of Purchase!Explanation / Answer
Let x is the amonunt of beer bottles you buy, and the bottles you see is y with probability 1/(2000-1000)=0.001(uniform probability). If x>y, then the profit is y*(5-2)+(x-y)*0.5=2.5y+x as you would have excess. If x<y, then profit is
x*(5-2)+(y-x)*0.2(because of shortage).=2.8x+y.
Expected total profir P(x>y)*(2.5y+x)+P(x<y)*(2.8x+y) and also P(x<y)=1-P(y>x) and as the probability is uniform,
P(x<y)=1/(y-1000), thus for optimal decision, expected profit=0, thus (1-1/(y-1000))*(2.5y+x)+1/(y-1000)*(2.8x+y)=0
solving this we get 2.5y+x+1/(y-1000)*(1.8x-1.5y)=0, now replace y with expected value of y which is 1500 to get the optimal decision, as x=500*0.2/0.7+1000=1142
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