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anonymous
 one year ago
PLEASE HELP!!!!
using the following system of inequalities find the maximum value of f(x,y)=3x+8y
x≥0
y≥0
3x+2y≤18
6x+7y≤42
anonymous
 one year ago
PLEASE HELP!!!! using the following system of inequalities find the maximum value of f(x,y)=3x+8y x≥0 y≥0 3x+2y≤18 6x+7y≤42

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Nnesha
 one year ago
Best ResponseYou've already chosen the best response.0you need to solve last two equations for y or just use desmos calculator shade the region

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0$$x\le 0\\y\le 0\\y\le \frac32 x+9\\y\le \frac67 x+6$$ dw:1438790372303:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the intersection is at $$\frac32 x+9=\frac67 x+6\\21x+14\cdot9=12x+14\cdot 6\\14\cdot 3=9x\\\frac{14}3=x$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so now we have the following points to test: $$x=0,\qquad y=0\\x=0,\qquad y=6\\x=0,\qquad y=9\\x=14/3,\ \ y=2\\x=6,\qquad y=0\\x=7,\qquad y=0$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oops, ot the \(x=0,y=9\) and \(x=7,y=0\), only the four points that bound the quadrilateral

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0plug these into your objective function and test them: $$f(0,0)=0\\f(0,6)=48\\f\left(\frac{14}3,2\right)=30\\f(6,0)=18$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438790959035:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the biggest value happened at \((14/3,2)\) with value \(30\), so \(30\) is our maximum value

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you so much !!!!
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