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Let F be the face of optimal solutions of the linear program max{cx: x ∈ P}, where P={x∈Rn:Ax≤b}. Let MF= be the equality set of F and let u* be any optimal solution of the dual linear program. Show that ui*=0 if i∉MF=.
The measure of angle A is 66 degrees and side c = 60 yd.
A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deep at the deep end. Water is being pumped into the pool at 1/4 cubic meter per minute, and there is 1 meter of water at the deep end.
A rectangular garden plot has dimensions of 15 ft. by 12 ft. A uniform path around the garden increases the total area to 270 sq. ft. What is the width of the larger rectangle?
Which of the following situations is inconsistent?
check to be sure that all deposits included in your record book are included and service charges are subtracted.make a
what percentage of the commuters will be using public transportation? (Round your answer to the nearest percent.)
Let f(x) = x^3, and compute the Riemann sum of f over the interval [6, 7], choosing the representative points to be the midpoints of the subintervals and using the following number of subintervals (n). (Round your answers to two decimal places.)
The supply curve for Florida is P = (1/3)Q. The supply curve for Oregon is P = 3 + (1/3)Q. What values of P and Q solve both these equations?
Determine the time it takes the ball to reach its maximum height:
The distance between the building and the pole is 189 ft, and the pole casts a shadow that is 4.25 ft long. How tall is the building?
Show that x^2+1 is irreducible as an element of Q[x] but reducible as an element of Z5[x]
Have you ever walked into a Wal-Mart store to find an item out of stock? Using the concepts discussed forecasting and in this module economic order quantity, address the following questions: How does Wal-Mart ensure that its shelves are always full? ..
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