A beer distributor incurs a penalty cost of $2 per case of shortage and a $1 charge per case left over in inventory at the of the week. assume that the demand (in number of cases ordered) follows the discrete distribution given in the table below.
demand probability
10 .2
20 0.3
30 0.3
40 0.1
50 0.1
a)what is the optimal number of cases to have on hand to minimize expected total costs in a single week? show calculations
b)what is the expected cost?