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Beft Co has been advised that the training has been extended for the painters into a second week. Beft has also been told that during that 2nd week, both metal and the paint supplier will be limiting their supplies to 36,000 kg of metal and 4,500L of paint.
Beft Co has decided to concentrate its activities on the square and oval plates and temporarily shut down the clover leaf production line. Their customers have been informed and Z Co has withdrawn its business, giving it 1 week’s notice.
Which TWO of the following statements are true?
1) Labour will have a shadow price of zero.
2) The objective function will be to maximise 15S + 15O, where S is the number of square plates and O is the number of Oval plates produced.
3) If solved graphically, the optimal solution will be where the constraints for metal and paint intersect.
4) Paint will have a positive shadow price.Answer
Number 2 & 4 are true.I haven’t copied out the whole question as I don’t think you need it to answer what I will ask but if you do let me know and I will copy it down
(1) I’m unsure how to approach this question. Do I need to make the constraints and make a graph in my workings, in order to find out if number 3 was true. Or is there a quicker way?
(2) The statement for number 2 I can see is the objective to maximise contribution. Is the question testing here that I know the contributions for S & O?
(3)
The examiner has shown some workings are as follows:Squre Oval
Metal 4kg 5kg
Paint 0.5L 0.75L
Hours-painting 0.5 hrs 1.5hrs
Maximum demand 4000 4500
Remove Z Co -500 -500
Total 3500 4000Maximum metal required = 3,500 units x 4kg + 4000 units x 5kg = 34,000kg – not binding
Maximum paint required = 3500 units x 0.5L + 4000 units x 0.75L = 4750 – binding condition
Maximum painting labour required = 3500 units x 0.5 hrs + 4000 units x 1.5hrs = 7750 – still a binding conditionMy first question is, what is this helping to work out?
In regards to the painting labour I am not sure how they know if it is a binding condition or not. Early on in the question it states that ‘Painting labour is limited to 7,250 hours for the next month while some workers are away on a training course.’ and now they have said at the beginning of this question that the training has been extended for a second week.
Thanks for your help. I have watched your lectures I am just still stuck!
I cannot answer your question because you have not typed the whole of the question.
I assume that this is a Section B type question, in which case you need the original information in the scenario to be able to answer it. (For example, earlier in the question it must have told you what the contribution per unit is. Also it must have told you what the maximum demands were. Both of these remain the same for all parts of the question).
As I explain in my lectures, you cannot be asked to draw a graph in the exam, and (assuming this question came from the current edition of a Revision Kit) the question cannot be expecting you to draw one (I assume that one is not drawn in the answer in the book).
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