Consider the optimization problem of maximizing Cobb–Douglas production function: Q = 20 K1/2 L1/2, subject to cost constraint: K + 4L = 64. a/ Use the method of Lagrange multipliers to find the maximum value of the production function;
b/ Estimate the change in the optimal value of Q if the cost constraint is changed to K + 4L = 65, and state the new maximum value of the production function.

The probability that a college student belongs to a health club is 0.3. the probability that a college student lives off-campus is 0.4. the probability that a college student belongs to a health club and lives off-campus is 0.12. find the probability that a college student belongs to a health club or lives off-campus. tip: p(a or b) = p(a) + p(b) - p(a and b) 0.54 0.58 0.70 0.82

Question 1 of 10 2 points different groups of 50 graduates of an engineering school were asked the starting annual salary for their first engineering job after graduation, and the sampling variability was low. if the average salary of one of the groups was $65,000, which of these is least likely to be the average salary of another of the groups? o a. $64,000 o b. $65,000 o c. $67,000 o d. $54,000

What is the value of x? enter your answer in the box. x =