XYZ works at Jamba juice and is responsible for inventing new products (drink) every year and maximizing profit for which she is paid off. This year, 2007 summer, he/she is considering producing a tea cooler that would be a blend of white tea, a green tea and fruit juice. To meet taste specifications, the tea cooler must consist of at least 50% white tea, at least 20% and no more than 30% green tea, and exactly 20% fruit juice. XYZ purchases the tea from local tea house and fruit juice from a processing plant in Sacramento. For the current production period, 10,000 gallons of white tea and 8,000 gallons of green tea can be purchased; an unlimited amount of fruit juice can be ordered. The costs for the tea are $1.00 for the white and $1.50 per gallon for the green; the fruit juice can be purchased for $0.50 per gallon.
Jamba juice can sell the entire tea cooler they can produce for $2.50 gallon.
a) formulate a linear program to determine the blend of three ingredients that will maximize the total profit contribution? Solve, interpretLINEAR PROGRAMMING PROBLEMMaximize Z =1.5W+1G+2FS.T.
1) 0.5W-0.5G-0.5F>02) -0.2W+0.8G-0.2F>03) -0.3W+0.7G-0.3F 0 ( % white tea)-0.2 + 0.8 g - 0.2f > 0 (% green minimum)-0.3w+ 0.7g- 0.3f < 0 ( % green maximum)-0.2w - 0.2g + 0.8f = 0 (fruit juice)W < 10000 (available white tea)G < 8000 (available green tea)W,G,F >0The output obtained using the management scientist to solve XYZ's invention of tea cooler and maximization of profit is shown in the above figure. The optimal solution calls for XYZ to purchase 10000 gallons of white tea, 6000 gallons of green tea, and 4000 gallons of fruit juice to maximize the profit. The value of the optimal solution or the total profit contribution Jamba juice will realize from this...