the steak and chop butcher shop purchases steak from a local meatpacking house.

Question

the steak and chop butcher shop purchases steak from a local meatpacking house. the meat is purchased on monday at $2.00 per pound, and the shop sells the steak for $3.00 per pound. any steak left over at the end of the week is sold to a local zoo for $.50 per pound. the possible demands for steak and the probability of each are shown in the following table:

***The shop must decide how much steak to order in a week. construct a payoff table for this decision situation and determine the amount of steak that should be ordered, using expected vale.

*** PLEASE SHOW WORK AND EXPLAIN***

I am pretty sure the EV is $21 and therefore 22 lbs should be purchased, but I am struggling to quantify why...

demand probability 20 .1 21 .2 22 .3 23 .3 24 .1

Explanation / Answer

From the given data,

E(X) = $22.1

Demand (x) P(X=x) x*P(X=x) 20 0.1 2 21 0.2 4.2 22 0.3 6.6 23 0.3 6.9 24 0.1 2.4 Total: 22.1

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