This document summarizes four examples from a lecture on quantitative analysis for business. The first example calculates average cost, cost deviation, covariance between cost and age, and cost increase per year for machine maintenance. The second example derives cost estimation equations for three machines that extrude plastic tubes based on tube length and setup costs. The third example estimates a linear model and price point to meet a weekly demand of 500 units based on demand at two given price points. The fourth example is not summarized.

1. Quantitative Analysis for Business Lecture 11 September 20th, 2010 http://www.slideshare.net/saark/ibm401-lecture-11

2. Example i Table on the left is cost of operating a machine at different age of the machine in years Find average cost of maintaining the machine How much does the cost deviate from year to year? Find sample covariance between cost and age How much does the cost increase each year? Estimate the operating costs of 0-year-old machine 10-year-old machine

3. Example ii Plastic tube is extruded from 3 machines according to tube length. Unit cost for tube is 20B per cm. The setup cost of as shown in table. Find cost estimation equation for all 3 machines List price for plastic tube from 1m to 15m.

4. Example iii At a unit price of $25, weekly demand for a product is 300 units. At a unit price of $40, the weekly demand is 150 units. Find an estimated linear model between weekly demand and unit price. What is the best estimation price point to meet weekly demand of 500 units?

5. Example iv

6. solutions

7. Example i Find average cost of maintaining the machine How much does the cost deviate from year to year? Find sample covariance between cost and age

8. Example i How much does the cost increase each year? Estimate the operating costs of 0-year-old machine 10-year-old machine

9. Example ii Find cost estimation equation for all 3 machines Cost = 200 + 20L for L < 5 Cost = 500 + 20L for 10 <= L <= 5 Cost = 800 + 20L for L > 10 List price for plastic tube from 1m to 15m.

10. Example iii Find an estimated linear model between weekly demand and unit price. Two conditions given for this relationship Demand = b0 + b1P 300 = b0 + b1(25) 150 = b0 + b1(40) Solving those 2 equations b0 = 550 b1 = -10 What is the best estimation price point to meet weekly demand of 500 units? P = (Demand – b0)/b1 P = (500 – 550)/(-10) = 5

11. Example iv

12. Example iv