Joe owns a small coffee shop, and his production function is q = 3kl where q is total output in cups per hour, k is the number of coffee machines (capital), and l is the number of employees hired per hour (labor). if joe's capital is currently fixed at k=3 machines, what is his short-run production function?

The monthly payment m of a loan of amount p for y years with an interest rate r can be calculated by the formula: m = p(r/12) 1 â’ (1 + r/12)â’12y calculate the monthly payment and the cummulative total payment for a $100,000 loan with an interest rate of 4.85% if taken out for 10 years, for 11 years, etc., up to a 30 year term. display the results in a three-column table where the first column is the number of years, the second is the monthly payment, and the third is the cummulative total payment. note: use format bank; for this problem. also, remember to represent the interest rate as a decimal (e. g. 0.0485) 2. a torus-shaped water tube is designed to have a volume of 8, 000in3 . the volume of the tube, v , and its surface area, s, are given by: v = 1 4 ď€ 2 (a + b)(b â’ a) 2 s = ď€ 2 (b 2 â’ a 2 ) if a = kb, determine s, a, and b for k = 0.2, 0.3, 0.7. display the results in a table

Consider each of the following cases: case accounting break-even unit price unit variable cost fixed costs depreciation 1 127,400 $ 38 $ 25 $ 711,000 ? 2 124,000 ? 41 2,500,000 $ 900,000 3 5,753 117 ? 171,000 100,000 required: (a) find the depreciation for case 1. (do not round your intermediate calculations.) (b) find the unit price for case 2. (do not round your intermediate calculations.) (c) find the unit variable cost for case 3. (do not round your intermediate calculations.)

In terms of the "great wheel of science", statistics are central to the research process (a) only between the hypothesis phase and the observation phase (b) only between the observation phase and the empirical generalization phase (c) only between the theory phase and the hypothesis phase (d) only between the empirical generalization phase and the theory phase