The Notip Table Company sells two models of its patented five-leg tables. The basic version uses...

The Notip Table Company sells two models of its patented five-leg tables. The basic version uses a wood top, requires 0.6 hour to assemble, and sells for a profit of $200. The deluxe model takes 1.5 hours to assemble because of its glass top, and sells for a profit of $350. Over the next week the company has 300 legs, 50 wood tops, 35 glass tops, and 63 hours of assembly available. Assuming that everything produced can be sold, you are asked to help Notip to determine a maximum-profit production plan.

(a) Formulate a mathematical programming model with 4 main constraints to select an optimal production plan using the following decision variables.

x" = number of basic models to be produced x# = number of deluxe models to be produced

(b) Solve your model to find the optimal product mix. What are the optimal x" and x# values? What is the maximum profit?
You may solve the model graphically by sketching out the constraints and objective function contour in a two-dimensional plot on Excel with the functions used and handwritten.

Expert Solution

Solution:

MAX Z = 200x1 + 350x2
subject to
5x1 + 5x2 <= 300
x1 <= 50
x2 <= 35
0.6x1 + 1.5x2 <= 63
and x1,x2 >= 0

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orchestra answered 2 years ago

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