Question 1208206: Formulate but do not solve the problem.
A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve. The time (in minutes) required by each department to produce a dozen blouses of each type is shown in the following table.
Sleeveless Short-sleeve Long-sleeve
Cutting 8 12 14
Sewing 22 23 28
Packaging 5 8 8
The cutting, sewing, and packaging departments have available a maximum of 80, 160, and 48 labor-hours, respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is operated at full capacity? (Let x, y, and z denote the amount of sleeveless, short-sleeve, and long-sleeve, respectively.)
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
Formulate but do not solve the problem.
A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve.
The time (in minutes) required by each department to produce a dozen blouses of each type is shown
in the following table.
Sleeveless Short-sleeve Long-sleeve
Cutting 8 12 14
Sewing 22 23 28
Packaging 5 8 8
The cutting, sewing, and packaging departments have available a maximum of 80, 160, and 48 labor-hours,
respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is
operated at full capacity? (Let x, y, and z denote the amount of sleeveless, short-sleeve, and long-sleeve,
respectively.)
~~~~~~~~~~~~~~~~~~~~~~~~~
Let x, y, and z denote the amount of sleeveless, short-sleeve, and long-sleeve, respectively, in dozens.
As you read the problem, you write three equations for three unknowns x, y and z
based on require time and given time limitations
8x + 12y + 14z = 80*60 (1) (the cutting department time limit, in minutes);
22x + 23y + 28z = 160*60 (2) (the sewing department time limit, in minutes);
5x + 8y + 8z = 48*60 (3) (the packaging department time limit, in minutes).
At this point, the setup is complete.
To solve, you may use manual technique like Gauss elimination or Cramer's method.
Alternatively, you may use technology (your calculator or online solvers).
Since the problem instructs "do not solve", I stop at this point.
Solved.
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To see many other similar solved problems, look into the lesson
- Solving word problems by reducing to systems of linear equations in three unknowns
in this site.
It is intended to make your horizon wider.
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