A furniture company makes dining room furniture. A buffet requires 42 minutes for construction and 42 minutes for finishing. A wooden dining room table takes 24 minutes for construction and 29 minutes for finishing. A wooden matching chair takes 12 minutes for construction and 11 minutes for finishing. Since the matching chairs go with the dining room table, they also need to manufacture 5 times as many chairs as tables. How many of each type of furniture should be manufactured if the company has 1428 worker minutes available for construction per week and 1428 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: ________ 2nd Equation for Finishing time: _______ 3rd Equation from the other given information: ________ 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= ________buffets ; y= _________ and z= _________ tables should be manufactured per week. c) How many of the infinite solutions are actually realistic for this problem? {Show your work in your Notes as demonstrated in the lecture videos on D2L.} _______________ realistic solutions d) Suppose they decide to manufacture 9 tables in one particular week. How many of each type of furniture can be made by the company during that week? ______ buffets, ________ chairs, and ________ tables can be manufactured.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
A furniture company makes dining room furniture. A buffet requires 42 minutes for construction and 42 minutes for finishing. A wooden dining room table takes 24 minutes for construction and 29 minutes for finishing. A wooden matching chair takes 12 minutes for construction and 11 minutes for finishing. Since the matching chairs go with the dining room table, they also need to manufacture 5 times as many chairs as tables. How many of each type of furniture should be manufactured if the company has 1428 worker minutes available for construction per week and 1428 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: ________
2nd Equation for Finishing time: _______
3rd Equation from the other given information: ________
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= ________buffets ;
y= _________ and
z= _________ tables should be manufactured per week.
c) How many of the infinite solutions are actually realistic for this problem? {Show your work in your Notes as demonstrated in the lecture videos on D2L.}
_______________ realistic solutions
d) Suppose they decide to manufacture 9 tables in one particular week. How many of each type of furniture can be made by the company during that week?
______ buffets, ________ chairs, and ________ tables can be manufactured.
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