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| linear programming |
aalkhodor |
12/09/06 |
A group of doctors are considering how best to economise on their prescriptions budget, whilst still serving their patients’ needs as well as they can. They present you with the following scenario.
“ We want to satisfy the minimum nutritional requirements of our 100 patients who need to take prescribed food supplements each month, whilst at the same time minimising the budgetary implications for our practice’s prescriptions budget. The Practice Manager has asked us to look carefully at this and we thought that you might be able to help.
Each food supplement drink that we prescribe contains four nutritional ingredients per large carton, as set out below
Drink A Drink B Drink C
Ingredient (fluid ounces)
DWW 10 30 16
EXX 4 3 20
FYY 2 16 5
GZZ 12 0 30
Cost per carton £20 £24 £15
Each month, the average patient who has been prescribed the food supplement cartons needs the following minimum intake of the special ingredients that are to be found in them:
DWW 1000 fluid ounces
EXX 500 fluid ounces
FYY 300 fluid ounces
GZZ 800 fluid ounces
Our patients cannot get these ingredients from any other food sources that are available to them. Unfortunately, we can only obtain a maximum of 25 cartons of Drink C each month for us to dispense, regardless of our need. This is because its flavour is regarded as much more palatable than that of Drinks A and B, by so many patients. Hence it is currently in very short supply. Can you help us here? What is the optimum mix of cartons that we should buy to meet our patients’ needs?”
REQUIRED:
1) Produce a report for the doctors, including a LP Formulation of the above problem. Explain the meaning of your Formulation and discuss any reservations that you may have about the assumptions underlying it and your potential findings.
( Can you please not post the answer to the public notice board, but only to me?)
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