1)
a.
Sheen should stock the optimal stocking quantity in this situation, which is 584
newspapers. The expected profit at this stocking quantity is $331.44.
b.
Q= µ+Φ
1
(C
u
/(C
u
+C
0
))δ
Q=500+ Φ
1
(.8/(.2+.8))100
Q=500+(.
.7881)(100)
Q=579
This is off by 5 newspapers from the model given in the spreadsheet, which
results in a $.03 difference in profits.
2)
a.
With the opportunity cost of her time per hour being equal to $10, Sheen should
invest 4 hours daily into the creation of the profile section. This would raise here
optimal stocking quantity to 685 newspapers and would increase her expected daily
profit to $371.33.
b.
Sheen’s choice of effort level,
h
, to be 4 hours was chosen because, in order to
maximize profit, she would need an effort level that made the marginal cost of her
effort equal to the marginal benefit. The marginal cost(opportunity cost) of her effort
was is $10/hr. The marginal benefit equated to (0.8 *50)/(2*√
h
). When set equal to
each other, the optimal # of hours invested comes out to be 4.
c.
The optimal profit under this model is greater because an increase the hours invested
in creating the profile section,
h,
is in direct relation to an increase in average daily
demand. With an increase in demand/sales, and no increase in fixed or variable costs,
profit will increase.
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a.
Armentrout’s optimal stocking quantity is equal to 516 newspapers. This creates of
channel profit of $322 and makes Anna’s profit equal to $260.20. This stocking
quantity maximizes Armentrout’s profit in this situation at $62.14.
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 Spring '10
 hora
 Economics, optimal stocking quantity, Armentrout

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