Consider the following linear programming problem. Min s.t. 4A + 7B 1A + 4B ≤ 21 2A + 1B27 3A +1.5B ≤ 21 -2A + 6B 20 A, B ≥ 0 (a) Find the optimal solution using the graphical solution procedure and the value of the objective function. at (A, B) = (b) Determine the amount of slack or surplus for each constraint. slack for 1A + 4B ≤ 21 surplus for 2A + 1B ≥ 7 slack for 3A + 1.5B ≤ 21 surplus for -2A + 6B ≥ 0 (c) Suppose the objective function is changed to max 8A + 3B. Find the optimal solution and the value of the objective function. at (A, B) =
Consider the following linear programming problem. Min s.t. 4A + 7B 1A + 4B ≤ 21 2A + 1B27 3A +1.5B ≤ 21 -2A + 6B 20 A, B ≥ 0 (a) Find the optimal solution using the graphical solution procedure and the value of the objective function. at (A, B) = (b) Determine the amount of slack or surplus for each constraint. slack for 1A + 4B ≤ 21 surplus for 2A + 1B ≥ 7 slack for 3A + 1.5B ≤ 21 surplus for -2A + 6B ≥ 0 (c) Suppose the objective function is changed to max 8A + 3B. Find the optimal solution and the value of the objective function. at (A, B) =
Practical Management Science
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Transcribed Image Text:Consider the following linear programming problem.
Min
s.t.
4A + 7B
1A + 4B ≤ 21
2A + 1B ≥7
3A + 1.5B ≤ 21
-2A + 6B ≥0
A, B≥ 0
(a) Find the optimal solution using the graphical solution procedure and the value of the objective function.
at (A, B):
=
(b) Determine the amount of slack or surplus for each constraint.
slack for 1A + 4B ≤ 21
surplus for 2A + 1B ≥ 7
slack for 3A + 1.5B ≤ 21
surplus for -2A + 6B ≥ 0
(c) Suppose the objective function is changed to max 8A + 3B. Find the optimal solution and the value of the objective function.
at (A, B)
=
Expert Solution
Objective Functions and Constraints:
Objective Functions and Constraints:
Based on the given details, the objective functions and constraints are
Objective Function:
Constraints:
Subject to
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