Question

Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pen...

Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below.

Fliptop Model Tiptop Model Available

Plastic 3 4 36

Ink Assembly 5 4 40

Molding Time 5 2 30

The profit for either model is $1000 per lot.

What is the linear programming model for this problem?

What are the boundary points of the feasible region?

What is the profitability at each boundary point of the feasible region?

Find the optimal solution.

Step 1

Let us assume that x_{1} amount of Fliptop and x_{2} amount of Tiptop models are produced, then the objective function is to maximize profitability with the constraints on the production limited by the available plastic, ink and time. Hence the LP model is given by the objective function and the three constraints as shown below:

Objective function ($) (OF): maximize z = 1000x_{1} + 1000x_{2}

Plastic material constraint ( Eqn. 1): 3x_{1} + 4x_{2} <= 36

Ink material constraint (Eqn. 2): 5x_{1} + 4x_{2} <= 40

Time constraint (Eqn. 3): 5x_{1} + 2x_{2} <= 30

Non negativity constraints: x_{1}, x_{2} >= 0

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