Consider the following distribution of scores with a mean of 80 and a standard deviation of 20. For the letters A, B, C, and D in the boxes beneath the line labeled “z” give the z-scores corresponding to each position in the distribution. One z-score is already filled in (–1). Suppose you also want to standardize these scores to a “k” scale where the mean of k is 50 and the standard deviation is 10. For the letters E, F, G, and H in the boxes beneath the line labeled “k” give the k-scores corresponding to each position in the distribution. One k-score is already filled in (60).

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.)