I just don't understand the way this question is solved. Can you please do it in a different way? Thanks.
A shoe producer makes a variety of footwear, including indoor slippers, children's shoes, and flip-flops. To keep up with increasing
demand, it is considering three expansion plans: (1) a small factory with yearly costs of $150,000 that will increase the production of flip-
flops to 400,000; (2) a: mid-sized factory with yearly costs of $250,000 that will increase the production of flip-flops to 600,000; and (3)
a large factory with yearly costs of $350,000 that will increase the production of flip-flops to 900,000. The profit per flip-flop is projected
to be $0.75. The probability distribution of the increased demand for flip-flops is provided. Let x represent the amount of profit the
producer will make.
Complete parts a through c below.
Small Plan E(x)= (Type an integer or a decimal.)
Mid-Sized Plan E(x) = (Type an integer or a decimal.)
Large Plan E(x) = (Type an integer or a decimal.)
b. Calculate the standard deviation for each of the expansion plans.
Small Plan Sigma(x) = (Round to the nearest whole number as needed.)
Mid-Sized Plan Sigma(x) = (Round to the nearest whole number as needed.)
Large Plan Sigma(x) = (Round to the nearest whole number as needed.)
c. Which expansion plan would you suggest Provide the statistical reasoning behind your selection.
The (a.large, b.small, c.mid-size) plan has the largest expected profit. This plan has a much (a.higher, b.lower) standard deviation than the
other plans so this would be a good choice for those who can absorb (a.less, b.more) risk than the other plans.
SOLUTION
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Small 150000 400000 300000 150000 200000 50%
Medium 250000 600000 450000 200000 333333 56%
Large 350000 900000 675000 325000 466667 52%
Small and Large have break even units at about 50% capacity