6) A fabric firm has received an order for cloth specified to contain at least 45 pounds of cotton and 25 pounds of silk. The cloth can be woven out of any suitable mix of two materials, A and B. Material A contains 30% cotton and 50% silk by weight and costs $3 per pound whereas Material B contains 60% cotton and 10% silk and costs $2 per pound. Let A represent quantities (in pounds) of Material A and let B represent quantities (in pounds) of Material B. What is the optimal combination of Material A and B to minimize costs? 7) Explain the underlying logic and philosophy of JIT. Illustrate with an example. 8) Why would qualitative forecasting be important when there is quantitative forecasting? Explain. How does poor forecasting adversely affect a firm's operations? Explain. 9) As shown below, actual demand for tools at a home improvement store has been increasing. If the forecast for the year 2001 is 28, find the forecast for the years 2002 up to 2006 using the exponential smoothing method with a smoothing constant of 0.7. Then try again using a smoothing constant of 0.8. Using M.A.P.D. and the data from 2002 to 2005, determine which smoothing constant allows for more accurate forecasting. (Show all your work. Round all numbers to one decimal place.) Year Demand 2001 30 2002 38 2003 2004 2005 54 60 78 10) Based on the data below, what is the projected demand level for Year 10? Year 1 2 3 4 5 6 7 8 9 Demand (Thousand) 17 16 16 21 20 20 23 25 24