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Question 981186: In order to solve this word problem i need to use the following strategies: Maximum or Minimum of an Objective Function, for a linear programming problem, and graph.
Directions Write the objective function and inequalities that describe the constraints in the problem. Graph the feasibility region, showing the corner points. Then find the maximum or minimum value of the objective function.
Making Furniture Problem: Two wood workers,Tom and Carlos, get $100 for making a table and $80 for making a chair. On average, Tom must work 3 hours and Carlos 2 hours to make a chair. Tom must work 2 hours and Carlos 6 hours to make a table. If neither wishes to work more than 42 hours per week, how many tables and how many chairs should they make each week to maximize their income. Find the maximum Income.
I attempted to do this problem using the required format. Made a chart that showed Table Chair Time Available
Income 100 80
Tom 2 3 42
Carlos 6 2 42
And made the following formula p=100x+80y with the following constraints
x+y lessthan/equal to 100 changes to y=-x+100
50x+y lessthan/equal to 40 " " y=-50x+100
x greaterthan/equal to 0
y greaterthan/equal to 0
Then graphed it literally 4 pages together to graph it and find the corner points.
Cornerpoints p=100x+80y
(0,0) 100(0)+80(0)=0
(0,40) 100(0)+80(40)= 3,200
(0,100) 100(0)+80(100)= 8,000
(1,99) 100(33)+80(67)= 8,600
That is the work i did, and the solution is suppose to be 3 tables, and 12 chairs, $1,260. Im not sure if i plugged this in wrong i used the formulas and examples in the book and even had some students taking precal help me and they agreed it was the correct way to set it up. I have no idea how to get that solution. Help Please.
Answer by solver91311(24713)   (Show Source):
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