Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. she has made an error in one of the steps below. find the step where joyce went wrong. step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one. step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one. step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one. step 4: x equals negative 8 plus or minus six all over two.

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i. e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)