Food | Vitamin A | Vitamin B | Vitamin C |
x | 1 | 2 | 3 |
y | 2 | 2 | 1 |
A) \[Rs.\,100\]
B) \[Rs.\,98\]
C) \[Rs.\,116\]
D) \[Rs.\,112\]
Correct Answer: D
Solution :
From the given data, we get the following LPP Min \[Z=16x+20y\] S.t. \[x+2y\ge 10,\] \[2x+2y\ge 12\] \[3x+y\ge 8\] and \[x\ge 0,\,\,y\ge 0\] First we assume all the inequalities as equationsEquations | Points |
\[x+2y=0\] | \[(0,\,5)\] and \[(10,\,0)\] |
s\[2x+2y=12\] | \[(0,6)\] and \[(6,0)\] |
\[3x+y=8\] | \[(0,8)\] and \[\left( \frac{8}{3},0 \right)\] |
Points | Objective function \[\min \,\,z=16x+20y\] |
\[T(0,\,8)\] | \[16\times 0+20\times 8=160\] |
\[S(1,\,5)\] | \[16\times 1+20\times 5=116\] |
\[Q(2,\,4)\] | \[16\times 2+20\times 4=112\](min) |
\[D(10,\,0)\] | \[16\times 10+20\times 0=160\] |
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