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December 6th, 2012, 01:53 PM   #1
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Need help with finance math problem

I have tried multiple variations of this problem numerous times, but keep getting the wrong answer. Please help me solve this.

A supplier for the automobile industry manufactures car and truck frames at two different plants. How many hours should each plant be scheduled to operate to exactly fill each of the orders listed below. The production rates (in frames per hour) for each plant are listed below as well.

Plant_A produces 7 car frames per hour and 2 truck frames per hour.
Plant_B produces 3 car frames per hour and 7 truck frames per hour.

Order_1 wants 1423 car frames and 812 truck frames.
Order_2 wants 1144 car frames and 548 truck frames.
Order_3 wants 1373 car frames and 1369 truck frames.

How many hours for Plant_A to fill Order_1 ???
How many hours for Plant_A to fill Order_2 ???
How many hours for Plant_A to fill Order_3 ???

How many hours for Plant_B to fill Order_1 ???
How many hours for Plant_B to fill Order_2 ???
How mahy hours for Plant_B to fill Order_3 ???
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December 6th, 2012, 01:56 PM   #2
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Re: Need help with finance math problem

It's not clear to me whether the car frames and truck frames are produced simultaneously or in serial. If the former, divide the number of frames by the production per hour for both cars and trucks and take the maximum. If the latter, take the sum instead of the maximum. In either case if production must be done in one-hour increments round up after the division.
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December 6th, 2012, 07:08 PM   #3
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Re: Need help with finance math problem

I wish it was as simple as that. This problem uses formulas and augmented matrices for the answer. Here is some details to the problem:

7x[1] + 3x[2] = k[1] (number of car frames)
2x[1] + 7x[2] = k[2] (number of truck frames)

The system of equations is written in matrix form.

[7,3_2,7][x[1]_x[2]] = [k[1]_k[2]]

To solve for x[1] and x[2], it is necessary to find the inverse of the 2 x 2 matrix shown above. To do this an augmented matrix is constructed with the 2 x 2 matrix to the left of the partition and the 2 x 2 identity matrix to the right of the partition.

[7,3_2,7|1,0_0,1]

Row 1 is divided by 7 to make the diagnal value in the first column equal to 1.

In order to make the element in row 2 column 1 equal 0, multiply row 1 by -3 and add the result to row 2.

-3R[1]+R[2]->R[2]

Using the inverted matrix, x[1] and x[2] can be determined.
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December 7th, 2012, 06:21 AM   #4
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Re: Need help with finance math problem

You can express it in terms of matrices, sure, but it's the same problem. That suggests my first interpretation, by the way: car and truck parts are produced simultaneously.
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December 7th, 2012, 06:53 AM   #5
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Re: Need help with finance math problem

Yes, you are right. Simultaneously
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December 7th, 2012, 12:45 PM   #6
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Re: Need help with finance math problem

Here is a link to the actual problem in question:

http://i672.photobucket.com/albums/v...thProblem1.jpg

These 2 other links are the first and second pages of the example steps on how to solve this type of problem.

http://i672.photobucket.com/albums/v...amplePage1.jpg
http://i672.photobucket.com/albums/v...amplePage2.jpg
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