Question

1. Solve the following linear programming model graphically: Maximize $4x_1 + 10x_2$ Subject to: $c_1: -5x_1 + x_2 le 0$ $c_2: -14x_1 + 11x_2 ge 0$ $c_3: 5x_1 + x_2 le 120$ $c_4: x_1 ge 12$ $x_1, x_2 ge 0$ (a) Create a graph clearly showing the feasible region. (b) Find the optimal decision variables and calculate the objective function value. Which constraints are binding? (c) The constant for decision variable $x_1$ is known to change over time. What is the maximum value the constant for $x_1$ can grow before the optimum point found in part (b) stops being optimum? (d) Constraint $c_3$ represents the availability of space to manufacture items $x_1$ and $x_2$. A project is proposed to expand the available space by 10 units. Should the project be undertaken? (e) Suppose both $x_1$ and $x_2$ are constrained to be integer numbers. What are the new optimum decision variables and the corresponding objective function value?

          1.
Solve the following linear programming model graphically:
Maximize $4x_1 + 10x_2$
Subject to:
$c_1: -5x_1 + x_2 le 0$
$c_2: -14x_1 + 11x_2 ge 0$
$c_3: 5x_1 + x_2 le 120$
$c_4: x_1 ge 12$
$x_1, x_2 ge 0$
(a) Create a graph clearly showing the feasible region.
(b) Find the optimal decision variables and calculate the objective function
value. Which constraints are binding?
(c) The constant for decision variable $x_1$ is known to change over time.
What is the maximum value the constant for $x_1$ can grow before the
optimum point found in part (b) stops being optimum?
(d) Constraint $c_3$ represents the availability of space to manufacture items $x_1$
and $x_2$. A project is proposed to expand the available space by 10 units.
Should the project be undertaken?
(e) Suppose both $x_1$ and $x_2$ are constrained to be integer numbers. What
are the new optimum decision variables and the corresponding objective
function value?

1.
Solve the following linear programming model graphically:
Maximize 4x1 + 10x2
Subject to:
c1: -5x1 + x2 le 0
c2: -14x1 + 11x2 ge 0
c3: 5x1 + x2 le 120
c4: x1 ge 12
x1, x2 ge 0
(a) Create a graph clearly showing the feasible region.
(b) Find the optimal decision variables and calculate the objective function
value. Which constraints are binding?
(c) The constant for decision variable x1 is known to change over time.
What is the maximum value the constant for x1 can grow before the
optimum point found in part (b) stops being optimum?
(d) Constraint c3 represents the availability of space to manufacture items x1
and x2. A project is proposed to expand the available space by 10 units.
Should the project be undertaken?
(e) Suppose both x1 and x2 are constrained to be integer numbers. What
are the new optimum decision variables and the corresponding objective
function value?

Added by Holly M.

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