Goop Inc. needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be normally distributed with a mean of 150 gallons and a standard deviation of 50 gallons. Goop sells the polymer for $39 per gallon. Goop purchases raw material for $23 per gallon and must spend $5 per gallon to dispose of all unused raw material due to government regulations. (One gallon of raw material yields one gallon of polymer.) If demand is more than Goop can make, then Goop sells only what it has made, and the rest of the demand is lost.

Round your answer to 2 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers.

The overage cost is $( ). The underage cost is $( ). The critical ratio is ( ) . Goop Inc. should order( ) gallons of this raw material to maximize its expected profit. In such case, the expected leftover inventory will be( ) gallons, the expected sales will be( ) gallons, and the expected profit will be( ) $ (use the standard normal table below).

The maximum profit of Goop Inc. is $( ).

If Goop Inc. orders 200 gallons, then the in-stock probability will be( ) %, the expected leftover inventory will be( ) gallons, the expected profit will be $( ), and the mismatch cost will be $( ) (use the standard normal table below)