Can you help on this linear programming question ?

Question

a)Northern Chip manufactures two models of minicomputers, the Alpha4 and the Beta5.  The firm employs 5 technicians, each working 160 hours every month, on the assembly line.  Management insists that full employment be maintained for each worker during next month’s operations.  It requires 20 labour-hours to assemble each Alpha4 computer and 25 labour-hours to assemble each Beta5 model.  There is no shortage of components other than specialized cooling fans.  The Alpha4 requires 2 such fans and the Beta5 requires 5 fans.  The company should have 130 in stock next month.  Northern Chip has firm orders for 10 Alpha4s and 15 Beta5s for the following month.  The estimated variable cost of production is £270 per Alpha4 and for Beta5 it is £450.  The retail price is currently set at £1470 for Alpha4 and £2250 for Beta5.


Determine the most profitable number of each model of minicomputer to produce during the coming month and hence the maximum monthly contribution to profits.  What are the limiting resource(s) for the company?

davemonpazier · Accepted Answer

I Have answered this withgouut using firmal linear planning tools
 Firstly , if possible you must manufacture to meet your firm orders
 that will take these resources
Man hours; 10 by 20 for the Alpha = 200 plus 15 times 25 =175 for the bata
 total 375
 That leaves 325 houes which you must use up
You will have used 20 fans dor the alpha and 75 for the beta,95 in all leaving 35 available

 The first attempt is to make 1 beta, 25 hours and hence 15 alpha, 300 hours
Rgis will use 5 fans forthe beta and 15 times 2 for tha alpha.
 Now this is not a very progitable solution, you are making more of the less profitable modal ( alpha profit is 1200 againsy 1800 for the beta) Given that you are selling 3 beta for 2 alpha, something needs too be done
Canyou change the ratio
 Now you hit a problem,;in order to use up all available man hours you need to make either 4 beta or 5 aloha for each 100 hours available; you must change the production in units of 100 hours or else you will not use all hours
so the next step up is tp make 5 beta  (125 hours) and 10 alphas.
 however thus requires 25 fans for the beta and 20 for the alpha; totak 45. You only have 35
Do the solution is far from satisfactory; you are constrained by the availability of cooling fans. However you are also constrained by the labour restriction;and management should consider negotiating a more flexible working hours scheduke. Consider, for example that the cost per man hour to produce an alpja is 13.5 pounds; for a beta 18. Incidentally, just in time manufacture would cut down on the capital required to homd stock both of finished items and also components

Can you help on this linear programming question ?

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