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May 7th, 2013, 11:51 PM   #1
Joined: Aug 2010

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Help Me Please!!

A company produces two products. Relevant information for each product is shown in Table 58. The company has a goal of $48 in profits and incurs a $1 penalty for each dollar it falls short of this goal. A total of 32 hours of labor are available. A $2 penalty is incurred for each hour of overtime (labor over 32 hours) used, and a $1 penalty is incurred for each hour of available labor that is unused. Marketing considerations require that at least 10 units of product 2 be produced. For each unit (of either product) by which production falls short of demand, a penalty of $5 is assessed.

a Formulate an LP that can be used to minimize the penalty incurred by the company
b Suppose the company sets (in order of importance) the following goals:

Goal 1 Avoid underutilization of labor
Goal 2 Meet demand for product 1
Goal 3 Meet demand for product 2
Goal 4 Do not use any overtime

Formulate and solve a preemptive goal programming model for this situation.

Product 1 Product 2
Labor required 4 hours 2 hours
Contribution to profit $4 $2

Marketing considerations require that at least 7 units of product 1 are produced and at least 10 units of product 2 are produced.

Can someone advice how to solve this?? Thanks in advance.
jonbryan80 is offline  
May 11th, 2013, 07:52 AM   #2
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Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,412
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Re: Help Me Please!!

Jon, your post is quite convoluted, plus (to me) makes little sense...

It has obviously been translated from another language:
are you SURE you're showing precisely the original?

4 hours/$4 is simply double 2hours/$2.
So, to keep this simple, we have 1 product that takes 6 hours and produces net income of $6.
Allowing even more hours, 36 instead of 32, then maximum without overtime is $36.
Can you give an example of how $48 is possible? I simply can't see how...

Perhaps I'm missing something
However, nobody else has answered, and it's been 3 days now since you posted this,
so looks like I'm not the only one that's confused
Denis is offline  

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