Solve the following linear programming model graphically Maximize 2x1 4x2 Subject to c1 2x1 x2 0 c2 2x1 2x2 50 c3 4x1 x2 145 c4 x1 30 x1,x2 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 decision variable x1 is known to change over time What is the maximum value x1 can grow before the optimum point found in part (b) stops being optimum (d) Constraint c4 represents the availability of a resource A contractor com pany has offered to supply extra 10 units of that resource Should it be accepted (e) Suppose both x1 and x2 are constrained to be integer numbers What are the new optimal decision variables and the new optimum function value

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Question: Solve the following linear programming model graphically: Maximize 2x1 + 4x2 Subject to: c1: 2x1+x2 0 c2: 2x1+2x2 50 c3: 4x1+x2 145 c4: x1 30

Solve the following linear programming model graphically:

Maximize 2x1 + 4x2

Subject to: c1: 2x1+x2 0

c2: 2x1+2x2 50

c3: 4x1+x2 145

c4: x1 30

x1,x2 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 decision variable x1 is known to change over time. What is the maximum value x1 can grow before the optimum point found in part (b) stops being optimum?
(d) Constraint c4 represents the availability of a resource. A contractor com- pany has offered to supply extra 10 units of that resource. Should it be accepted?
(e) Suppose both x1 and x2 are constrained to be integer numbers. What are the new optimal decision variables and the new optimum function value?

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