anonymous
  • anonymous
In the graph below, the set of inequalities 10P + 15 D ≤ 300 1 P< 6 2 D ≥ 12 3 were drawn and the feasible region of the set of inequalities is shaded in grey. Determine the maximum value of the function F =6P + 20D subject to the set of inequalities above.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
|dw:1378708379737:dw|
anonymous
  • anonymous
I think I found my answer, do I just calculate all the vertices and then substitute them into the function F?
ganeshie8
  • ganeshie8
Maximum value occurs at one of the vertex of shaded region

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ganeshie8
  • ganeshie8
exactly ! test all the vertices of that shaded region
anonymous
  • anonymous
Thanks for the clarification.
anonymous
  • anonymous
So in this case the maximum will be 400 at the vertex (0, 20)?
ganeshie8
  • ganeshie8
you have 4 vertices here : (0, 12) , (0, 20) , (6, 12) and wats the fourth vertex ?
anonymous
  • anonymous
12, 12
ganeshie8
  • ganeshie8
no, fourth vertex must be like this (6, _ )
anonymous
  • anonymous
12, 6 it looks like it should be
anonymous
  • anonymous
6, 12 sorry
ganeshie8
  • ganeshie8
|dw:1378709819720:dw|
anonymous
  • anonymous
|dw:1378709858293:dw|
ganeshie8
  • ganeshie8
for 4th vertex, you need to solve the equations, 10P+ 15D = 300 P = 6 yes, solving them gives you (6, 16)
anonymous
  • anonymous
|dw:1378709928403:dw|
ganeshie8
  • ganeshie8
looks good :)
ganeshie8
  • ganeshie8
we test each vertex in the objective function, F = 6P+20D
ganeshie8
  • ganeshie8
(6, 16) F = 6(6) + 20(16) = 356
anonymous
  • anonymous
Now iv solved for them all in the F funtion and I get F(6, 16) = 356, F(6, 12)=276, F(0, 20) = 400, F(0, 10) = 200
ganeshie8
  • ganeshie8
Yes :) so you're rihgt, 400 is the max value of funciton subject to given constraints ! good work .. !!
anonymous
  • anonymous
Thanks man, you helped a lot.
ganeshie8
  • ganeshie8
np :)

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