Questions for calculus

Q1 (3 marks ) Find two positive numbers such that their product is 192 and the sum of the first plus three times the second is a minimum.

Q2 (4 marks) A rectangle has its base on the x-axis and its upper two vertices on the parabola y=12-x^2. For all such rectangles, what are the dimensions of the rectangle with the largest area?

Q3 (4 marks) Given the cost function C(x)=1280+4x+0.02X^2, and the demand function p(x)=20+80/x, find the number of units produced in order to have maximum profit. (Be sure to confirm that this is a maximum )