how many sandwiches of each size should be made to maximize profit?

Question

Sam's deli makes snadwiches using bread and meat. Each regular sandwich uses 6 inches of bread and 2 ounces of meat, while each large sandwhich uses 10 inches of bread and 4 ounces of meat. THe profit on a small sandwich is $0.80 and on a large sandwich is $1.20. If the deli has 110 feet of bread and 30 pounds of meat, how many sandwiches of each size should be made to maximize profit?

Answer 1

The delicatessen has 1,320" (110' · 12"/foot) of bread.

 

According to the given data, a 6" sandwich yields $0.80 profit, and a 10" sandwich yields $1.20 profit.

 

So, a 6" sandwich yields $0.133 profit per inch ($0.80 ÷ 6")

and a 10" sandwich yields $0.12 per inch ($1.20 ÷ 10")

 

In view of those figures, in order to maximize profit, the owner of the delicatessen should make ONLY 6" sandwiches. Any other combination will result in less profit.