Minimize C=5x+4y Given The Constraints | Wyzant Ask An Expert

Subject ZIP Search Search Find an Online Tutor Now Ask Ask a Question For Free Login Solving for minima Maxima Minimize C=5x+4y given the constraints 0<=x<=6 0<=y<=6 4x+2y<=8 2x+y>=4   Follow • 3 Add comment More Report

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Best Newest Oldest By: Best Newest Oldest Minimize C=5x+4y given the constraints0<=x<=60<=y<=64x+2y<=82x+y>=4 I will do this by Solver, is easy and a modern way of solving this. Anyone knowing Excel knows the tool. Objective Cell (Min) Cell Name Original Value Final Value $B$10 eq 10 10 Variable Cells Cell Name Original Value Final Value Integer $B$11 x 2 2 Contin $B$12 y 0 0 Contin The answer is: the minimum value of the equation is 10 To obtain this the values of the variables are: x=2 Y=0 Satisfying the following Constraints: Cell Name Cell Value Formula Status Slack $B$13 8 $B$13<=8 Binding 0 $B$14 4 $B$14>=4 Binding 0 $B$11 x 2 $B$11<=6 Not Binding 4 $B$11 x 2 $B$11>=0 Not Binding 2 $B$12 y 0 $B$12<=6 Not Binding 6 $B$12 y 0 $B$12>=0 Binding 0 Upvote • 1 Downvote Add comment More Report Hi Chalyce, The first thing I think we should do is examine the 4 constraints. #1 and #2 tell us that the solution for the minimum C must come from the 6x6 square in the x-y plane bounded by (0,6) for both x and y. Now let's look at #3: 4x + 2y <= 8. We can divide all terms by 2 to get: 2x + y <= 4. Now let's move the x-term to the right side: y <= 4 - 2x. If we plot y = 4 - 2x on top of our 6x6 square, we have a line cutting off a small triangle near the (0,0) origin. For the "<" part of <=, this means the solution is constrained for (x,y) on the line or inside the triangle. Now we look at the 4th constraint: 2x + y >= 4. Again, let's get the x-term to the right side: y >= 4 - 2x. For the "=" part of >=, this is exactly the same line as constraint #3 !! But the ">" tells us that we are constrained by the line and the trapezoid above the line. To honor constraints #3 & #4, the only part in common is simply the line y = 4 - 2x. I hope you have plotted this line on our 6x6 square for constraints #1 & #2. If you did, you see that x ranges from 0 to 2. We'll need that information soon ... Last step: we know our solution space is the line y = 4 - 2x. We can insert this into our function-to-minimize as follows: C = 5x + 4y, with y = 4 - 2x so, C = 5x + 4(4 - 2x) = 5x + 16 - 8x = 16 - 3x I'll leave the rest for you -- we know C = 16 - 3x, and x ranges from 0 to 2. Please help me by telling what the minimum C is, and the (x,y). Thanks, Pete Upvote • 1 Downvote Comment • 1 More Report Report

08/04/14

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