Question

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

​$1010

on each bronze​ package,

​$3030

on each silver​ package, and

​$5050

on each gold package. The food wholesaler has a total of

80008000

bags of regular​ chips,

37003700

bags of​ barbeque, and

16001600

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 1x1​,

x 2x2​,

and

x 3x3

represent the numbers of​ bronze, silver, and gold packages made​ up, respectively, and let z be the total profit.

 

▼   Minimize Maximize	zequals=nothing
subject to	20 x 1 plus 20 x 2 plus 30 x 320x1+20x2+30x3	▼   less than< greater than> less than or equals≤ greater than or equals≥	nothing
	10 x 1 plus 10 x 2 plus 10 x 310x1+10x2+10x3	▼   greater than> greater than or equals≥ less than< less than or equals≤	nothing
	10 x 2 plus 10 x 310x2+10x3	▼   less than or equals≤ greater than> greater than or equals≥ less than<	nothing
	x 1x1greater than or equals≥​0, x 2x2greater than or equals≥​0, x 3x3greater than or equals≥0.

​(Do not factor. Do not include the​ $ symbol in your​ answers.)