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Concept explainers
A furniture manufacturer builds tables. The cost for materials and labor to build a kitchen table is
Let
a. Write an objective function representing the monthly profit for producing and selling
b. The manufacturing process is subject to the following constraints. Write a system of inequalities representing the constraints.
• The number of each type of table cannot be negative.
• Due to labor and equipment restrictions, the company can build at most
• The company can build at most
• The company does not want to exceed a monthly cost of
c. Graph the system of inequalities represented by the constraints.
d. Find the vertices of the feasible region.
e. Test the objective function at each vertex.
f. How many kitchen tables and how many dining room tables should be produced to maximize profit? (Assume that all tables produced will be sold.)
g. What is the maximum profit?
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