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5 and a half pounds of chocolate chip cookies are to be packed into bags each of which holds a third of a pound. How many bags will be filled and how much will be left for the packer to munch on?

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Related questions

A food wholesaler has three kinds of individual bags of potato​ chips: regular,​ barbeque, and salt and vinegar. She wants to sell the bags of chips in bulk packages. The bronze package consists of 20 bags of regular and 10 bags of barbeque. The silver package contains 20 bags of​ regular, 10 bags of​ barbeque, and 10 bags of salt and vinegar. The gold package consists of 30 bags of​ regular, 10 bags of​ barbeque, and 10 bags of salt and vinegar. The profit is
​$10
on each bronze​ package,
​$30
on each silver​ package, and
​$50
on each gold package. The food wholesaler has a total of
8000
bags of regular​ chips,
3700
bags of​ barbeque, and
1600
bags of salt and vinegar. Assume all the packages will be sold. Use the simplex method to complete parts​ (a) and​ (b).
​(a) How many​ gold, silver, and bronze packages should be made up in order to maximize​ profit? What is the maximum​ profit?
 
Set up the linear programming problem. Let
x 1​,
x 2​,
and
x 3
represent the numbers of​ bronze, silver, and gold packages made​ up, respectively, and let z be the total profit.
 
 
Minimize
Maximize
zequalsnothing
subject to
20 x 1 plus 20 x 2 plus 30 x 3
 
less than
greater than
less than or equals
greater than or equals
nothing
 
10 x 1 plus 10 x 2 plus 10 x 3
 
greater than
greater than or equals
less than
less than or equals
nothing
 
10 x 2 plus 10 x 3
 
less than or equals
greater than
greater than or equals
less than
nothing
 
x 1greater than or equals​0,
x 2greater than or equals​0,
x 3greater than or equals0.
​(Do not factor. Do not include the​ $ symbol in your​ answers.)

A certain drug dosage calls for 5 mg per kg per day and is divided into three doses (1 every 8 hours). If a person weighs 165 pounds, how much of the drug should be administered each time?

A certain drug dosage calls for 5 mg per kg per day and is divided into three doses (1 every 8 hours). If a person weighs 165 pounds, how much of the drug should be administered each time?

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