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May 7th, 2013, 11:51 PM  #1 
Newbie Joined: Aug 2010 Posts: 27 Thanks: 0  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. 
May 11th, 2013, 07:52 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  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 