Quiz #1 name: ..matric no. question 1 (a6 marks, b-5marks,.c-5mark let -fur l)-100 2 2y dente the prodaction foction specifying th ber of units of output that can be produced uing positeve inputs of k its of capital and l of labour (a) compute fl, 1). a4,9) and f16, 25) b) show tat fx 1-2pu l), and give an ecouomic interpretation () show in geaeral that fk, l)-tfk l) for all t> 0

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.)