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I don’t understand why in this exam question the graph produces a result to show 6,000 pool cues should be made. When I solve using simultaneous equations (which should theoretically produce the same result) I get 12,000 for snooker cues but 8000 for pool. If you multiply 0.27 by 8000 plus 0.27 by 12,000 you get 2160+3240 which is 5,400. So why does the graph show 6,000 for pool cues? The answer also mentions a 3 month period – where does it mention this in the question….?
Many Thanks
Further to the above what’s the best way to solve the simultaneous equation….
P0.5+S0.75=12,000
P0.27+S0.27=5400Does it matter which way round you do it..?
With regard to your first question, we always have to use simultaneous equations to get the optimum solution (you cannot just read it from the graph). However you need the graph to decide which is the optimum solution and therefore which equations to solve.
Your solution will not work. If you produce 12,000 snooker and 8,000 pool, then the total time needed will be (12,000 x 0.75) + (8,000 x 0.5) which is equal to 13,000 hours. But there are only 12,000 hours available, so this is not possible!!
You cannot find the answer simply by calculating for all the combinations of constraints. You must draw the graph (partly because it is needed, but also because the question specifically asks for it). From the graph you can decide the optimum point and then use simultaneous equations to calculate how many of each product.
With regard to the three months, you are correct. The question simply refers to a ‘period’. So ignore the three months in the answer – it does not matter how long the ‘period’ is, it will not affect the answer.
With regard to your second question, there are many ways of solving two simultaneous equations and it does not matter how you do it. There is only one answer that results, but how you do it does not matter. (People are taught different ways at school – use whatever way you are most happy with 🙂 )
Thank You – so graph first and then either simultaneous equations to find the absolute values or as per this question we know the value for X so just substitute this into the equation 🙂 much appreciated
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