Based on the assigned textbook reading for this week, as well as the InstructorInsight document that I posted, I composed an example of a LinearProgramming$($LP$)$ model in the form of a word problem for you to consider.Your assignment is to read the problem presented here and then formulateTWO linear inequality constraints and an objective function, for this model,based on the information presented. This is a typical LP scenario for models thatwe will be discussing in week $4.$Based on your reading, challenge yourself to formulate the mathematicalconstraints and objective function for this problem.Compose and submit your responses using an MS Excel spreadsheet, using thecolumns to define the constraint, inequality sign, and value of the constraint,restating the problem and detailing the mathematical logic involved toformulate the constraints and the objective function.Present the constraints$($linear inequality format$)$ and objective function, whichwill serve as the basis for graphing of the constraints and allow for themaximization of the objective function.You are not being asked to graph or solve this problem. ONLY define theconstraints and objective function.Instructor Hint: $-$ Formulation of the problemThe question asks for the number of cabinets that you will need to buy.In all of these type of LP models, you will need to define the variables that you willuse in the constraints and objective function.

In the model that I am presenting to you here, the variables will be defined as:x: number of model X cabinets purchasedy: number of model Y cabinets purchasedThe assumption in this model will be that, x $>0$ and y $>0,$ based on the logicalassumption that you cannot purchase negative amounts of cabinets.As defined in the problem description below, you will need to consider costsand floor space $($the "footprint" of each unit$),$ while maximizing the storagevolume$($the objective function$).$ Therefore, costs and floor space will be theconstraints, while volume will be the optimization or objective function.Both constraint equations are going to be in the form of an inequality. I leave it toyou to determine the type of inequality. The objective function will not be in theform of an inequality. Inequality signs can be entered into an equation, either inan MS Word of Excel doc, using the $$symbols$$ tab in word or excel. To insert asymbol in Word, place your cursor where you want the symbol to appear in yourdocument. Then click the $$Insert$$ tab in the Ribbon. Then click the $$Symbol$$button in the $$Symbols$$ button group to display a drop$-$down menu of the mostcommonly used symbols.Just so you don$$t get all stressed out with formulating this mathematical LPmodel, I posted a document this week in the folder titled, $$Generic LP Model$,$as a generic example of the formulation of a two$-$constraint model and anobjective function, for you to consider as the basis for formulating theconstraints and objective function for the problem below.Sometimes I wonder why I take the time and make the effort to give you asmuch information as possible to address these assignments. So if you thank mesome time for my efforts, it would make my day!

Assigned Problem Scenario:

You need to buy some filing cabinets. You know that Cabinet X costs $$10$ perunit, requires six square feet of floor space, and holds eight cubic feet of files.Cabinet Y costs $$20$ per unit, requires eight square feet of floor space, and holdstwelve cubic feet of files. You have been given $$140$ for this purchase, thoughyou don't have to spend that much. The office has room for no more than $72$square feet of cabinets. How many of which model should you buy, in order tomaximize storage volume?