Use the linear programming diagram below to answer the question that follow. y B (c,d) Feasible set A D X 0 (e, 0) (f,0) Not drawn to scale Consider the linear progamming problem for the objective function f(x, y) = 30x + 42y. The function is optimised subject to the constraints below. The constraints which bound the feasible set are shown in the diagram above. A (a, b) C Consider the linear progamming problem for the objective function f(x, y) = 30x + 42y. The function is optimised subject to the constraints below. The constraints which bound the feasible set are shown in the diagram above. 12y ≤ - 4 + 20x (AB in the figure) -21y ≤ 336 + 12x (AC in the figure) -24y - 1376 + 32x (BD in the figure) X ≥0 y ≥0 (a) Find the coordinates of the corner points A, B, C and D. Coordinates of A (x, y) = ( Coordinates of B (x, y) = (

Use the linear programming diagram below to answer the question that follow. y B (c,d) Feasible set A D X 0 (e, 0) (f,0) Not drawn to scale Consider the linear progamming problem for the objective function f(x, y) = 30x + 42y. The function is optimised subject to the constraints below. The constraints which bound the feasible set are shown in the diagram above. A (a, b) C Consider the linear progamming problem for the objective function f(x, y) = 30x + 42y. The function is optimised subject to the constraints below. The constraints which bound the feasible set are shown in the diagram above. 12y ≤ - 4 + 20x (AB in the figure) -21y ≤ 336 + 12x (AC in the figure) -24y - 1376 + 32x (BD in the figure) X ≥0 y ≥0 (a) Find the coordinates of the corner points A, B, C and D. Coordinates of A (x, y) = ( Coordinates of B (x, y) = (

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Consider the linear progamming problem for the objective function
f(x, y) = 30x + 42y.
The function is optimised subject to the constraints below. The
constraints which bound the feasible set are shown in the diagram above.
12y ≤ - 4 + 20x (AB in the figure)
-21y ≤ 336 + 12x (AC in the figure)
-24y - 1376 + 32x
(BD in the figure)
X ≥0
y ≥0
(a) Find the coordinates of the corner points A, B, C and D.
Coordinates of A (x, y) = (
Coordinates of B (x, y) = (

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Follow-up Question

(c) Find the slope of the objective function.
Slope =
(d) What are the values of x and y that give the maximum value of f(x, y)?
X =
y =
(e) What is the maximum value for f(x, y)?
Suppose that the objective function is now f(x, y) = 230x - 100y
(f) Find the slope of the objective function.
Slope =
(g) What are the values of x and y that give the maximum value of f(x, y)
in this case?
X =

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