i.
To calculate: A florist is creating 10 centerpieces. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. The customer has a budget of $300 allocated for the centerpieces and wants each centerpiece to contain 12 flowers, with twice as many roses as the number of irises and lilies combined. Write a system of linear equations that represents the situation. Then write a matrix equation that corresponds to your system.
i.
Answer to Problem 65E
The systems of equations are
Explanation of Solution
Let R be the number of roses, L be the number of lilies and I be the number of irises. First we know that the total number of flowers is 120.
The budget of flowers is $300 and roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each.
Now, the last condition is that there should be twice as many roses as the number of irises and lilies combined.
Then from above 3 equations a system of matrix is formed
ii.
To calculate: A florist is creating 10 centerpieces. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. The customer has a budget of $300 allocated for the centerpieces and wants each centerpiece to contain 12 flowers, with twice as many roses as the number of irises and lilies combined. Solve your system of linear equations using an inverse matrix. Find the number of flowers of each type that the florist can use to create the 10 centerpieces.
ii.
Answer to Problem 65E
Hence Roses=80, Lily=10, and Iris=30.
Explanation of Solution
From part (a) we have
The above system of equation can be written as
Now find the inverse of matrix A
Solve above system of equation using Gauss-Jordan elimination method
Further
As
Chapter 8 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning