Solve the following linear programming problem involving two variables by the graphical method (a) Find the maximum value of the objective function Z = 4x + 6y where x ≥ 0 and y ≥ 0, subject to the constraints -X+ y≤ 11 2x + 5y ≤ 90 x + y ≤ 27 (12 marks) (b) An airline offers coach and first-class tickets. For the airline to be profitable, it must sell a minimum of 25 first-class tickets and a minimum of 40 coach tickets. The company makes a profit of $225 for each coach ticket and $200 for each first-class ticket. At most, the plane has a capacity of 150 travelers. Determine how many of each ticket should be sold in order to maximize profits. Objective Function: P= 225x + 200y Constraints: y≥ 25 x≥ 40 x+ y≤ 150 x ≥ 0 and y >0
Solve the following linear programming problem involving two variables by the graphical method (a) Find the maximum value of the objective function Z = 4x + 6y where x ≥ 0 and y ≥ 0, subject to the constraints -X+ y≤ 11 2x + 5y ≤ 90 x + y ≤ 27 (12 marks) (b) An airline offers coach and first-class tickets. For the airline to be profitable, it must sell a minimum of 25 first-class tickets and a minimum of 40 coach tickets. The company makes a profit of $225 for each coach ticket and $200 for each first-class ticket. At most, the plane has a capacity of 150 travelers. Determine how many of each ticket should be sold in order to maximize profits. Objective Function: P= 225x + 200y Constraints: y≥ 25 x≥ 40 x+ y≤ 150 x ≥ 0 and y >0
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
Solve the following linear programming problem involving two variables by the graphical
method
(a)
Find the maximum value of the objective function Z = 4x + 6y
where x ≥ 0 and y ≥ 0, subject to the constraints
-X+ y≤ 11
2x + 5y ≤ 90
x + y ≤ 27
(12 marks)
(b)
An airline offers coach and first-class tickets. For the airline to be profitable, it must
sell a minimum of 25 first-class tickets and a minimum of 40 coach tickets. The
company makes a profit of $225 for each coach ticket and $200 for each first-class
ticket. At most, the plane has a capacity of 150 travelers. Determine how many of
each ticket should be sold in order to maximize profits.
Objective Function: P= 225x + 200y
Constraints: y≥ 25
x≥ 40
x+ y≤ 150
x ≥ 0 and y >0
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