(in Stat 250 introduction to Operation Research
)
pls help
thanks?
Solution to question no. 10
let us denote grano and wheatie by x and y respectively.
According to the constraints,
Space constraint : 0.2x + 0.4y = 60
Demand Constraint : x =< 200 , y =< 120.
To maximaize profit Z = 1x+1.35y under the above constraints.
If only X: then Xmax = 60/0.2 = 300 ; If only Y: then Ymax = 150.
Putting the demand constraints, x =< 200 , y =< 120.
So, intersection of these give the extremum points.
{x,y} : {60,120} or {200,50}
Profit at {60,120} = 60*1 + 120*1.35 = 222
profit at {200,50} = 200*1 + 50*1.35 = 267.5
SO maximum profit is found when 200 boxes of Grano and 50 boxes of wheatie are kept.
space allocation in this situation = 200 * 0.2 = 40 sqft. = 66.67% for grano
and 50 * 0.4 = 20 sqft which is 33.33% for wheatie.
Thus, i disagree with the space allocation done.
Note: By Providing 43% and 57% respectively, the profit made would be = 244 approx
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