1 A company manufactures scientific calculators. The cost of manufacturing one calculator in a batch of size x can be modelled by the function C(x) = 0.01x10x + 150. The company wants to minimize the cost of producing the calculators. Find the size of the batch for which the cost per calculator is minimized. 2 A pharmaceutical company's research department proposes a mathematical model which connects the amount of a blood pressure drug that is injected into a patient (x cm) with the decrease in the patient's systolic pressure (the highest pressure when the heart beats, f(x) mmHg) The model is f(x)=x-x Determine the amount of medication that produces the largest drop in the systolic pressure, and the size of this systolic drop. 3 The production costs of x USB flash drives made by a company can be modelled by the function c(x) = 500 + 3x. The projected selling price is mdelled by p(x)=7-0.002x. The projected revenues therefore can be modelled by the function r(x) = x(7-0.002x).