This problem shows why the dual variable for an equality constraint should be urs. a Use the rules given in the text to find the dual of
max z = xy + 2x2
s. t. 3x1 + x2 ≤ 6
2x1 + x2 = 5
X1, X2 ≥ 0
b. Now transform the LP in part (a) to the normal form.
Use y and y as the dual variables for the two pri- mal constraints derived from 2x1 + x2 = 5.
c. Make the substitution y2 = y - y2 in the part (b) answer. Now show that the two duals obtained in parts (a) and (b) are equivalent.

To ? nd out how many students are unhappy with the dining hall food, you distribute a survey. which method of surveying would produce the least amount of bias in your data?

Christine wong has asked dave and mike to her move into a new apartment on sunday morning. she has asked them both, in case one of them does not show up. from past experience, christine knows that there is a 40% chance that dave will not show up and a 30% chance that mik a. what is the probability that both dave and mike will show up? (round your answer to 2 decimal places.) b. what is the probability that at least one of them will show up? c. what is the probability that neither dave nor mike will show up? (round your answer to 2 decimal places.)e will not show up. dave and mike do not know each other and their decisions can be assumed to be independent.

After reading 80% of her e-mails in her inbox, danette still has m unread e-mails. which of the following expressions could represent the number of e-mails danette had in her inbox before she started reading? choose 2 answers: (choice a) 5m (choice b) 1.8m (choice c) 80m (choice d) m/0.8 (choice e) m/1−0.8