An engineer performs a flow test of a cooling water system. the test equipment hooks into flow elements in the system. there are 32 flow elements. for each flow element she needs two 3 feet lengths of polyflow tubing with quick release connectors on each end. both lengths of polyflow tubing plug into a test gauge to measure the flow across each flow element. each test gauge is $80. the 3/16" polyflow tubing is $6.00 for 100 feet the connectors are $2.50 each. the budget for the test is $3,000.00. after buying the necessary equipment, how much under budget should she be?

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0