Coffee Blends A coffee merchant sells two different coffee blends. The Standard blend uses 4 oz of arabica and 12 oz of robusta beans per package; the Deluxe blend uses 10 oz of arabica and 6 oz of robusta beans per package. The merchant has 80 lb of arabica and 90 lb of robusta beans available. Find a system of inequalities that describes the possible number of Standard and Deluxe packages the merchant can make. Graph the solution set.
The system of inequalities for the total number of standard and deluxe package the merchant make and sketch the graph for solution set.
Answer to Problem 53E
The system of inequalities that describes the production of standard and deluxe package by the merchant is
Explanation of Solution
Given:
Let the number of standard coffee package made by the merchant be x
Let the number of deluxe blend coffee made by the merchant be y
Total number of oz of arabica merchant contains is
Total number of robusta merchant contains is 1440
Total Arabica required by both standard and deluxe coffee should not greater than
The first inequality is
Total robusta required by both standard and deluxe coffee should not exceed
The second inequality is
The number of standard and deluxe coffee is not negative
Take the first inequality
To plot the graph change the sign of inequality
Substitute 0 for x in
Substitute 0 for y in
Take the second inequality
To plot the graph change the sign of inequality
Substitute 0 for x in
Substitute 0 for y in
The point of intersection between the first two inequality
Multiply the first equation
Subtract the second equation from first,
Substitute
Figure (1)
Thus, system of inequalities that describes the production of standard and deluxe package by the merchant are
Chapter 10 Solutions
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