Question 9. We continue discussing the equations of (2]. We start at the point P where 125 = :35 = 3:;- = 1123 = 0. Before we considered exchanging :35 for a new basis variables. Did 1:1 get larger or smaller as a result? If we exchanged 1:5, 3:7 or :33, would :31 become larger or smaller? How can we determine this without nding the exact coordinates of the new points? If you've gotten this far, you should know how to: 0 Start at a point with a basis of variables that are U, forming the pivot columns of a row reduced matrix. 0 Determine whether exchanging one of those basis variables will increase or decrease the objective function. 0 Exchange a basis variable in order to increase the objective flmction, and put the equations into row reduced echelon form with respect to the new basis. The simpler algorithm. is to continue in this manner, always performing basis exchanges which improve the objective flmction, Imtil no more exchanges are possible. We conclude with an example: Buzz Buzz Buzz Coffee has on hand 1 kg of coffee grounds, 1 gallon of milk and 10 cups of sugar. They.r can use these to make espressos, containing 8 grams of grounds and no milk or sugar; lattes, containing 15 grams of grounds, 0.0625 gallons of milk and 0.125 cups of sugar; or cafe cubano, containing 7.5 grams of grounds, no milk and 0.125 cups of sugar. They will be able to sell all they produce, which they will sell at prices of $2 for espressos, $4 for lattes and $5 for cafe cubano