Consider a feasible solution x to the standard form problem minimize c 0x subject to ax = b x ≥ 0, and let z = {i : xi = 0}. show that x is an optimal solution if and only if the linear programming problem minimize c 0 d subject to ad = 0 (1) di ≥ 0, i ∈ z, has an optimal cost of zero

Marco has $38.43 dollars in his checking account. his checking account is linked to his amazon music account so he can buy music. the songs he purchases cost $1.29. part 1: write an expression to describe the amount of money in his checking account in relationship to the number of songs he purchases. part 2: describe what the variable represents in this situation.

Askyscraper is 396 meters tall. at a certain time of day, it casts a shadow that is 332 meters long.at what angle is the sun above the horizon at that time?

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.)