5. Certain laboratory animals must have at least 30 grams of protein and at least 20 grams of fat per feeding period. These nutrients come from food A, which costs 18 cents per unit and supplies 2 grams of protein and 4 of fat, and food B, with 6 grams of protein and 2 of fat, costing 12 cents per unit. Food B is bought under a long-term contract requiring that at least 2 units of B be used per serving. How much of each food must be bought to produce the minimum cost per serving? (15%)
6. From a potential committee pool with 8 Hispanic, 6 Caucasian, and 3 African-American members, 4 members are to be selected. (10%)
(a) Find the probability that 2 Hispanic, 1 Caucasian and 1 African-American are selected.;
(b) How many different ways can 4 members be selected if the 1st member selected is to be paid at $10 for serving the committee, the 2nd member selected at $8, the 3rd at $6, while the 4th does not get paid.
7. From the problem 6 above, if two members are to be selected, what is the expected number of Hispanic members that will be chosen?. Let x be the number of Hispanic members selected. Hint: First construct a probability distribution for x, then find the expected value. (20%)
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