A large bakery can produce rolls in lots of either 0,1000,2000 or3000 per day. T

Question

A large bakery can produce rolls in lots of either 0,1000,2000 or3000 per day. The production cost per item is $0.10. The demandvaries randomly according to the following distribution:
demand forrolls                    0        1000      2000       3000
probability ofdemand          0.3        0.2         0.3          0.2

Every roll for which there is a demand is sold for $0.30. Everyroll for which there is a no demand is sold in a secondary marketfor $0.05. How many rolls should the bakery produce each day to maximize the mean profit?

Explanation / Answer

Step 1    Find the Total Cost of Producing each lot ofrolls (quanity x cost) Lotssize      0      1000      2000      3000 Totalcost    0      $100       $200      $300 Step 2    Determine the number of rolls that willbe sold for demand price and the number that will not be sold fordemand price.  (Times the probability of demand andthe size of the lot to get the number of rolls demanded) Demandfor rolls                              0                        1000                  2000         3000 Probability ofdemand                     0.3                        0.2                     0.3            0.2 # of rolls sold at demandprice      (0x0.3)=0         (1000x0.2)=200      600            600 # of rolls sold in secondarymkt       0                    (1000-200)=800     1400          2400 Step 3    Find the Revenue from each lot of rolls(Revenue = price x quanity), remember there are 2 differentprices. demand price = $0.30 secondary mkt price = $0.10 # of rolls sold at demandprice      0      200      600      600 # of rolls sold in secondarymkt     0     800      1400     2400 Revenue Demandprice                              0      $60       $180     $180     Secondarymkt                            0      $40        $70       $120 TotalRevenue                             0      $100      $250     $300 Step 4    Find the profit (profit = revenue -cost) lot size      0      1000      2000      3000 revenue    0      $100      $250      $300 cost         0       $100      $200     $300 profit        0         0            $50         0 To make the highest profit the bakery should make 2000 rollsper day     

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