Chapter 3 Practice test Optimization:

Knowledge:

1.A rectangle is to be placed in the first quadrant, with one side on the x-axis and one side on the y-axis, so the rectangle lies below the line 2y+6x=18 . Determine the dimensions of the rectangle that will yield a maximum area. (4marks)

2. Determine two positive numbers whose product is 100 and whose sum is as small as possible. (4 marks)

3. The cost, in dollars, to produce x lamps for a certain factory is C(x) = 300 + 23x + 0.4x ^ 2, x_> 100

What is the marginal cost at 250 lamps? (2 marks)