SOLUTION: A company makes 2 types of chairs: basic chair and a deluxe chair. In One day the company can make at most 150 chairs total. The company can make at most 100 basic chairs and at mo
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Question 637391: A company makes 2 types of chairs: basic chair and a deluxe chair. In One day the company can make at most 150 chairs total. The company can make at most 100 basic chairs and at most 75 deluxe chairs.The company makes $12 profit for each basic chair and $8 profit for each deluxe chair. Let x represent the number of basic chairs made in one day and y represent the number of deluxe chairs made in one day. Use linear programming to determine the maximum possible profit for one day. Show the steps for the linear programming method as requested. Write the system of the inequalities that represent the situation.
I could really use help with this problem im not understand AT ALL! Answer by solver91311(24713) (Show Source):
Let represent the number of basic chairs manufactured in a given day. Let represent the number of deluxe chairs made.
The profit function is then
The constraints are:
The last constraint is that the values of the variables must be integers since you have to sell whole chairs; any possible fractional part of a chair could not be part of the solution.
Graph each of the constraint inequalities on one set of axes. The pentagonal (5-sided) area where the solution sets ALL overlap is the area of feasibility.
The optimum point is one of the vertices of the feasibility polygon. Test the coordinates of each of the vertices in the Objective (Profit) function. The set of coordinates that gives you the largest profit value is the optimum solution.
John
My calculator said it, I believe it, that settles it
