Miguel and jake run a paper company. each week they need to produce 1,000 reams of paper to ship to their customers. the paper plant's long-run production function is q = 4k^0.75l^0.25 , where q is the number of reams produced, k is the quantity of capital rented, and l is the quantity of labor hired. for this production function, the mpl = k^0.75 / l^0.75 and the mpk = 3l^0.25 / k^0.25 . the weekly cost function for the paper plant is c = 10k + 2l, where c is the total weekly cost
a. what ratio of capital to labor minimizes jake and paul's total costs?
b. how much capital and labor will jake and paul need to rent and hire in order to produce 1,000 reams of paper each week?
c. how much will hiring these inputs cost them?

11.     before adding cream to a simmering soup, you need to a. simmer the cream. b. chill the cream. c. strain the cream through cheesecloth. d. allow the cream reach room temperature. student d   incorrect which answer is right?

Popeye produces 20 cans of spinach in 8 hours. wimpy produces 15 hamburgers in 10 hours. if each hamburger trades for 1.5 cans of spinach, then: a.wimpy’s production and productivity are greater than popeye’s. b.popeye’s production is greater than wimpy’s, but his productivity is less. c.wimpy’s production is greater than popeye’s, but his productivity is less. d.popeye’s production and productivity are greater than wimpy’s.

Aproduction line has three machines a, b, and c, with reliabilities of .96, .86, and .85, respectively. the machines are arranged so that if one breaks down, the others must shut down. engineers are weighing two alternative designs for increasing the line’s reliability. plan 1 involves adding an identical backup line, and plan 2 involves providing a backup for each machine. in either case, three machines (a, b, and c) would be used with reliabilities equal to the original three. a. compute overall system reliability under plan 1. (round your intermediate calculations and final answer to 4 decimal places.) reliability b. compute overall system reliability under plan 2. (round your intermediate calculations and final answer to 4 decimal places.) reliability c. which plan will provide the higher reliability? plan2plan1