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.