QUESTION 8 20 points Save Answer A Pharmaceutical company produces two types of

Question

QUESTION 8 20 points Save Answer A Pharmaceutical company produces two types of drug composites called X and T using from two rw materials R1 & R2. The requirement of raw material for these drug composites as well as thoir availablity siong with the profit per tons is given in the following table Tons of Raw Material In Tons Maximum Availability/day tons) 24 Raw Material R1 Raw Material R2 Profit/Ton Market survey indicates that the daily demand for T cannot exceed that of X by more than 1 ton Also, maximum daily demand of T is 2 tons Determine the optimal product mix that maximizes totai daily proft

Explanation / Answer

Maximum Daily Demand of T cannot exceed more Than 2 Units and also cannot exceed that of X by more than 1 Unit

Number of X unit/day= R1X+R2X

Number of T unit/day= R1T+ R2T

X

T

Capacity

R1

6*R1X

4*R1T

24

R2

1*R2X

2*R2T

6

Object Function is to Maximise the Profit:

Max: X 5*(R1X+R2X) +4*(R1T+ R2T)

Subject To:

R1X+R2X- R1T- R2T<=1

R1T+ R2T<=2

6*R1X+4*R1T<=24

1*R2X+2* R2T<=6

Solution vector x:

   R1X= 2.6667

R2X= 0.3333

R1T= 2.0000

R2T= 0.0000

Objective function f(x) =    23.0000

Hence total of X unit = 3 and T = 2 a Day

X

T

Capacity

R1

6*R1X

4*R1T

24

R2

1*R2X

2*R2T

6

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