Mechanics and Techniques Problems

14.1. The function c(q) = 0.1q + 3 + represents the average cost for producing q of a product. (Assuming that q > 0.) Find the minimum average cost and the number of goods that should be produced in order to achieve this minimum.

14.2. The function c(q) = - 2.250 + 0.000328q gives the average cost for producing q goods.

1. Find a formula for the total cost of producing q goods by multiplying the average cost function by the number of goods produced.
2. Find the minimum total cost and the number of goods that should be produced in order to achieve this minimum total cost.

14.3. Given the points (1, 12), (2, 7), (3, 5) and (4, 6), assume that a linear function fits these points. Assume that the linear function passes through the point (x,y) so that the y-intercept, A, is given by A = y - Bx where B is the slope of the least-squares regression line.

1. Write down the exact error function, E(B), as a function of slope for the total squared error between the data points and the regression line.
2. Minimize your total squared error function to find the slope of the least-squares regression line. Show all steps and explain all work.