Mixed Nuts Nola’s Nuts, a store that specializes in selling nuts, has available 90 pounds (lb) of cashews and 120 lb of peanuts. These are to be mixed in 12-ounce (oz) packages as follows: a lower-priced package containing 8 oz of peanuts and 4 oz of cashews, and a quality package containing 6 oz of peanuts and 6 oz of cashews. a. Using x to denote the number of lower-priced packages, and use y to denote the number of quality packages. Write a system of linear inequalities that describes the possible numbers of each kind of package. b. Graph the system and label the corner points.
Mixed Nuts Nola’s Nuts, a store that specializes in selling nuts, has available 90 pounds (lb) of cashews and 120 lb of peanuts. These are to be mixed in 12-ounce (oz) packages as follows: a lower-priced package containing 8 oz of peanuts and 4 oz of cashews, and a quality package containing 6 oz of peanuts and 6 oz of cashews. a. Using x to denote the number of lower-priced packages, and use y to denote the number of quality packages. Write a system of linear inequalities that describes the possible numbers of each kind of package. b. Graph the system and label the corner points.
Solution Summary: The author explains how to write a system of linear inequalities that describes the possible numbers of packages of each kind of package and graph the system and label the corner points.
Mixed Nuts Nola’s Nuts, a store that specializes in selling nuts, has available 90 pounds (lb) of cashews and 120 lb of peanuts. These are to be mixed in 12-ounce (oz) packages as follows: a lower-priced package containing 8 oz of peanuts and 4 oz of cashews, and a quality package containing 6 oz of peanuts and 6 oz of cashews.
a. Using
to denote the number of lower-priced packages, and use
to denote the number of quality packages. Write a system of linear inequalities that describes the possible numbers of each kind of package.
b. Graph the system and label the corner points.
Expert Solution & Answer
To determine
To find:
1. To write a system of linear inequalities that describes the possible numbers of packages of each kind of package.
2. To graph the system and label the corner points.
Answer to Problem 60AYU
Solution:
Explanation of Solution
Formula Used:
Given:
Cashews
Peanuts
Lower priced packages
4oz
8oz
Quality packages
6oz
6oz
Store has of cashews and of peanuts.
Calculation:
Begin by assigning symbols for the two variables.
Because and represents the number of packages, the only meaningful values of and are non–negative.
Therefore,
From the given data and the formula used we get
Therefore, a system of linear inequalities that describes the possible amounts of each investment are
2. The graph of the system and corner points are illustrated in the figure below.
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