A furniture company makes dining room furniture. A buffet requires 40 minutes for construction and 40 minutes for finishing. A wooden dining room table takes 36 minutes for construction and 40 minutes for finishing. A wooden matching chair takes 11 minutes for construction and 10 minutes for finishing. Since the matching chairs go with the dining room table, they also need to manufacture 4 times as many chairs as tables. How many of each type of furniture should be manufactured if the company has 1280 worker minutes available for construction per week and 1280 minutes available per week for finishing? Set up a system of equations, and then solve it using your calculator and the matrix features
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A furniture company makes dining room furniture. A buffet requires 40 minutes for construction and 40 minutes for finishing. A wooden dining room table takes 36 minutes for construction and 40 minutes for finishing. A wooden matching chair takes 11 minutes for construction and 10 minutes for finishing. Since the matching chairs go with the dining room table, they also need to manufacture 4 times as many chairs as tables. How many of each type of furniture should be manufactured if the company has 1280 worker minutes available for construction per week and 1280 minutes available per week for finishing? Set up a system of equations, and then solve it using your calculator and the matrix features. {Show all work, including your system of equations, in your Notebooks as demonstrated in class.}
a) Let xx represent the number of buffets, yy represent the number of chairs, and zz represent the number of tables manufactured in a given week. Create a system of 3 equations from the constraints listed above. Type your equations here:
1st Equation for Construction time: 40x+11y+36z=1280
2nd Equation for Finishing time: 40x+10y+40z=1280
3rd Equation from the other given information: y=4z
b) There are actually an infinite number of solutions to this system. Write the solutions here, using tt as the parameter as needed. Solution:
x=x= 32−2t buffets ;
y=y= 4t chairs ; and
z=z= t tables should be manufactured per week.
c) How many of the infinite solutions are actually realistic for this problem? (Show ALL your work in your Notes as to how you came up with that answer!)
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