A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero units of protein, 3 units of carbohydratos, and 2 units of fat, and will contain 40 calories. Each ounce of nuts will supply 3 units of protein, 2 units of carbohydrates, and 4 units of fat, and will contain 50 calories. Every package must provide at least 3 units of protein, at least 11 units of carbohydrates, and no more than 14 units of fat. Find the number of ounces of fruit and number of ounces of
nuts that will meet the requirement with the least number of calories. What is the least number of calorios?
Let x be the ounces of fruit and y be the ounces of nuts. What is the objective function that must by minimized?
z=(?)x+(?)y

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)