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8. [-/2 Points] DETAILS WANEFMAC7 6.5.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Solve the standard minimization problem using duality. (You may already have seen some of them in earlier sections, but now you will be solving them using a different method.) Minimize c = s + t subject to s + 4t 2 40 4s + t 2 40 s 20, t 2 0. C = (s, t) =7. [-/7 Points] DETAILS WANEFMAC7 6.1.019. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Sketch the region that corresponds to the given inequalities. 16x + 8y s 80 8x + 16y s 80 8x + 8ys 48 x 2 0, y 20 10 10 Solution Set Solution Set - X -10 -5 5 10 -10 -5 10 -51 -5 -10 -10 y y 10 10 Solution Set Solution Set X -10 -5 5 10 -10 -5 5 10 -5 -5 -10 Say whether the region is bounded or unbounded. The region is bounded. O The region is unbounded. Find the coordinates of all corner points (if any). (Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.) ( x, y) = ( (x, y) =( ( x, y ) = ( x , y ) = (x, y ) = (2. [-/2 Points] DETAILS WANEFMAC7 6.3.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Maximize p = 14x + 10y + 12z subject to x+ y - z s 12 x + 2y + z s 32 x+ y s 20 x 20, y 2 0, Z 2 0. P = ( x, y, Z ) =6. [-/2 Points] DETAILS WANEFMAC7 6.5.018. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Solve the standard minimization problem using duality. (You may already have seen some of them in earlier sections, but now you will be solving them using a different method.) Minimize c = s + t + 2u subject to s + 5t + 2u 2 108 5s + t + 3u 2 108 s 20, t 2 0, u 2 0. C = (s, t, u) =