Milk proteins are sometimes added to sausage to reduce shrinking due to cooking loss and improve the texture of the sausage. Suppose the cooking loss (expressed as a percentage of initial weight) can be modeled by percent, where w is the proportion of whey protein and s is the proportion of skim milk powder. Determine whether the function L has a relative maximum, relative minimum, or a saddle point, and find the corresponding proportions of whey protein and skim milk powder at that point. Round your answer to the nearest hundredth of a percent.
A) relative maximum Whey protein: 5.62% Skim milk powder: 5.04%
B) relative minimum Whey protein: 5.62% Skim milk powder: 5.04%
C) relative maximum Whey protein: 19.83% Skim milk powder: 17.78%
D) relative maximum Whey protein: 17.78% Skim milk powder: 19.83%
E) saddle point Whey protein: 17.78% Skim milk powder: 19.83%

Question

Milk proteins are sometimes added to sausage to reduce shrinking due to cooking loss and improve the texture of the sausage. Suppose the cooking loss (expressed as a percentage of initial weight) can be modeled by  percent, where w is the proportion of whey protein and s is the proportion of skim milk powder. Determine whether the function L has a relative maximum, relative minimum, or a saddle point, and find the corresponding proportions of whey protein and skim milk powder at that point. Round your answer to the nearest hundredth of a percent.
A) relative maximum Whey protein: 5.62% Skim milk powder: 5.04% 
B) relative minimum Whey protein: 5.62% Skim milk powder: 5.04% 
C) relative maximum Whey protein: 19.83% Skim milk powder: 17.78% 
D) relative maximum Whey protein: 17.78% Skim milk powder: 19.83% 
E) saddle point Whey protein: 17.78% Skim milk powder: 19.83%

Quizplus · Accepted Answer

The function L is of the form 11e^(aw+bs), where a and b are negative constants. This function has a saddle point at (w,s)=(a/(a+b), b/(a+b)). Plugging in the values given, we get (w,s)=(0.1778,0.1983). Therefore, the answer is E, saddle point.

Milk Proteins Are Sometimes Added to Sausage to Reduce Shrinking