My Math Forum (HELP!) Gauss-Jordan Method Word Problem

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 February 27th, 2018, 09:53 AM #1 Newbie   Joined: Feb 2018 From: Virginia Posts: 1 Thanks: 0 (HELP!) Gauss-Jordan Method Word Problem Don't even know where to start with this one - I think I have to take the given information and create a system, but I don't even understand how with the way it is worded. I'm supposed to be using the Gauss-Jordan Method. Here's all of the information. Question: You are charged with the purchasing decisions at a local branch for a retail store. You have to make a decision on investing in lighting and shelving for the upcoming quarter.There are two brands of lights available for purchase, say: Brand A, Brand B. Also, there are two brands of shelves available for purchase: Brand C and Brand D. The branch has a usable surface area of 4000 sq ft. You work out the following about the various items: - Each unit of Brand A light has an initial cost of \$120 and provides enough light for 600 sq ft. of in store area. We expect it will consume \$20 monthly in electricity and maintenance. - Each unit of Brand B light has an initial cost of \$160 and provides enough light for 800 sq ft. of in store area. We expect it will consume \$40 monthly in electricity and maintenance. - Each unit of Brand C shelving costs \$400 and has surface dimensions 100 × 10 (width x height in feet), and stores, monthly, about \$1000 worth of stock that will be sold at an average of \$1200. - Each unit of Brand D shelving costs \$600 and has surface dimensions 160 × 10 (width x height in feet) , and stores, monthly, about \$1400 worth of stock that will be sold at an average of \$1800. You can assume that: •the entirety of the usable surface area of the store needs to be lit •the business needs to remain profitable every regular month (i.e. not accounting for the initial fixed cost) •the entirety of your budget of \\$2000 needs to be spent on initial fixed costs. Then answer the following questions and clearly explain your arguments: a. How many of each item should we purchase in order to guarantee profitability at the end of every month? (not accounting for initial fixed costs) b. In the best possible scenario, how many months will be required to break even with the initial fixed costs of buying all the items? Hint: Introduce two extra variables, say p and d, for, respectively, the regular monthly profit and the free in-store area space left after placing all the shelves. Anyone, please. Help a girl out. Last edited by skipjack; February 27th, 2018 at 12:57 PM.
 March 5th, 2018, 12:03 PM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 Let "u" be the number of units of A lighting purchased and let "v" be the number of units of B lighting purchased. Then we can light 600u+ 800v square feet. We must have 600u+ 800v= 4000 which is equivalent to 3u+ 4v= 20. Let "x" be the number of units of shelving C purchased and let "y" be the number of units of shelving D purchased. The total initial costs are 120u+ 160v+ 400x+ 600y= 2000 which is equivalent to 3u+ 4v+ 10x+ 15y= 50. The lights cost 20u+ 40v monthly while the shelves bring in a profit of 200x+ 400y. The store will earn 200x+ 400y- 20u- 40v each month.

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