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Lab 9 – Math 2355 – Spring 2016 (14pts) Name: ______________________________________ Discussion Section:__________ Due Date: Friday, April 22nd, by 8:30am The purpose of Lab 9 is to "put it all together." There are 2 problems. Solve them using techniques learned in previous labs. BE SURE TO PRINT PAGES WHEN ASKED TO DO SO AS THEY ARE WORTH POINTS. Insert a new sheet at the end of your file and name it “L9 #1”. Problem 1: The Tubular Ride Boogie Board Company has manufacturing plants in Tucson, Arizona, and Toronto, Ontario. You have been given the job of coordinating distribution of the latest model, the Gladiator, to their outlets in Honolulu and Venice Beach. The Tucson plant, when operating at full capacity, can manufacture 620 Gladiator boards per week, while the Toronto plant, beset by labor disputes, can produce only 410 boards per week. The outlet in Honolulu orders 500 Gladiator boards per week, while Venice Beach orders 530 boards per week. Transportation costs are as follows: Tucson to Honolulu: $10 per board; Tucson to Venice Beach: $5 per board; Toronto to Honolulu: $20 per board; Toronto to Venice Beach: $10 per board. Your manager has informed you that the company’s total transportation budget is $6550. You realize that it may not be possible to fill all the orders, but you would like the total number of boogie boards shipped to be as large as possible. Given this, how many Gladiator boards should you order shipped from each manufacturing plant to each distribution outlet? Let x1 = ______________________________________________________ x2 = ______________________________________________________ x3 = ______________________________________________________ x4 = ______________________________________________________ Constraint 1: _______________________________________________________ Constraint 2: _______________________________________________________ Constraint 3: _______________________________________________________ Constraint 4: _______________________________________________________ Constraint 5: _______________________________________________________ Nonnegative Constraints: _____________________________________________ Objective function :________________________________Max or Min? Use Solver… to find the solution. On the Answer report sheet, type your name in cell E1, your Wnumber in cell E2. Do not alter any other information on the sheet. Print this sheet. Be sure to attach it to your lab as it is worth points. State the final solution by writing a few brief sentences. 2 Insert a new sheet at the end of your file and name it “L9 #2”. Problem 2: A car rental company has four locations in the city: Northside, Eastside, Southside, and Westside. The Westside location has 20 more cars than it needs, and the Eastside location has 15 more cars than it needs. The Northside location needs 10 more cars than it has, and the Southside location needs 25 more cars than it has. It costs $10 (in salary and gas) to have an employee drive a car from Westside to Northside. It costs $5 to drive a car from Eastside to Northside. It costs $20 to drive a car from Westside to Southside, and it costs $10 to drive a car from Eastside to Southside. If the company will spend a total of $475 rearranging its cars, how many cars will it drive from each of Westside and Eastside to each of Northside and Southside? (a) Let x = ___________________________________________ y = ___________________________________________ z = ___________________________________________ w = ___________________________________________ (b) Formulate the matrix equation (with dimensions A5x4, X4x1 and B5x1) associated with the problem. (c) Use inverse matrix operations to find the solution. Please answer using a complete sentence. Type your name in cell G1 and print this page. It should show the information from part (b) along with all of the associated steps and the solution to the problem.