operations management •• 12.51 Cynthia Knott’s oyster bar buys fresh Louisiana oysters for $5 per pound and sells them for $9 per pound. Any oysters not sold that day are sold to her cousin, who has a nearby grocery store, for $2 per pound. Cynthia believes that demand follows the normal distribution, with a mean of 100 pounds and a standard deviation of 15 pounds. How many pounds should she order each day?

Question

operations management  •• 12.51 Cynthia Knott’s oyster bar buys fresh Louisiana oysters for $5 per pound and sells them for $9 per pound. Any oysters not sold that day are sold to her cousin, who has a nearby grocery store, for $2 per pound. Cynthia believes that demand follows the normal distribution, with a mean of 100 pounds and a standard deviation of 15 pounds. How many pounds should she order each day?

oobleck · Answer

If she buys x oysters and has y left over, then her profit is
9(x-y)-5x+2y = 4x-7y
So, if her goal is to break even, she needs y = 4/7 x
That is, she needs to sell at least 3/7 of he oysters.
If she has some other goal, then that must be adjusted.

Now you can play around with the Z-table, and a good place is

http://davidmlane.com/hyperstat/z_table.html