A garden shop sells two kinds of mixtures for planting. A package of gardening mixture requires 2 pounds of soil, 1 pound of peat moss, and 1 pound of fertilizer. A package of potting mixture requires 1 pound of soil, 2 pounds of peat moss, and 3 pounds of fertilizer. The shop has 16 pounds of soil, 11 pounds of peat moss, and 15 pounds of fertilizer. If a package of gardening mixture sells for $3.00, and a package of potting mixture for $5.50, how many of each should the shop make to maximize the revenue? What is the maximum revenue? Complete parts (a) through (e). (a) Complete the following table. Gardening Mixture Number of packages Pounds of soil Pounds of peat moss Pounds of fertilizer Revenue per package ($) (Type an integers or decimals.) (b) Set up the corresponding linear programming problem. Maximize z= (Type integers or decimals.) subject to: X S 16 11 S 15 x 2 0 y z 0 (Type expressions using x and y as the variables.) S Potting Mixture Maximum Amount
A garden shop sells two kinds of mixtures for planting. A package of gardening mixture requires 2 pounds of soil, 1 pound of peat moss, and 1 pound of fertilizer. A package of potting mixture requires 1 pound of soil, 2 pounds of peat moss, and 3 pounds of fertilizer. The shop has 16 pounds of soil, 11 pounds of peat moss, and 15 pounds of fertilizer. If a package of gardening mixture sells for $3.00, and a package of potting mixture for $5.50, how many of each should the shop make to maximize the revenue? What is the maximum revenue? Complete parts (a) through (e). (a) Complete the following table. Gardening Mixture Number of packages Pounds of soil Pounds of peat moss Pounds of fertilizer Revenue per package ($) (Type an integers or decimals.) (b) Set up the corresponding linear programming problem. Maximize z= (Type integers or decimals.) subject to: X S 16 11 S 15 x 2 0 y z 0 (Type expressions using x and y as the variables.) S Potting Mixture Maximum Amount
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:(c) Choose the correct graph of the feasible region of the system of constraints.
O A.
B.
(d) Evaluate the objective function at each corner point.
orner Points
(0, 0)
(3, 4)
Value of z
O C.
(0,5)
(7,2)
(8,0)
(Type an integers or decimals.)
(e) How many packages of gardening mixture and potting mixture should the shop make to maximize the revenue? What is the maximum revenue?
The shop should make packages of the gardening mixture and packages of potting mixture for a maximum revenue of $
Transcribed Image Text:A garden shop sells two kinds of mixtures for planting. A package of gardening mixture requires 2 pounds of soil, 1 pound of peat moss, and 1 pound of fertilizer. A package of potting mixture
requires 1 pound of soil, 2 pounds of peat moss, and 3 pounds of fertilizer. The shop has 16 pounds of soil, 11 pounds of peat moss, and 15 pounds of fertilizer. If a package of gardening mixture
sells for $3.00, and a package of potting mixture for $5.50, how many of each should the shop make to maximize the revenue? What is the maximum revenue? Complete parts (a) through (e).
(a) Complete the following table.
Gardening Mixture
Maximize Z=
Number of packages
Pounds of soil
Pounds of peat moss
Pounds of fertilizer
Revenue per package
($)
(Type an integers or decimals.)
(b) Set up the corresponding linear programming problem.
0
X +
(Type integers or decimals.)
subject to:
X
S 16
11
15
X >
0
y ≥
0
(Type expressions using x and y as the variables.)
S
Potting Mixture
y
Maximum Amount
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
