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Date Created: 11/15/15
Running Head TWO VARIABLE 1 TwoVariable Inequality name MAT 221 Introduction to Algebra Linda Seeger Date TWO VARIABLE 2 TwoVariable Inequality An inequality is an equation that can be used to determine if something is equal to less than or greater than something else By using inequalities we can figure out the relative size of two values and judge based on the inequality if they are big or small or there is too much or not enough of a given object For instance if a bakery receives an order where the customer wants to receive cupcakes and cakes the baker would use a specific amount of our for each cake and cupcakes It takes one and a half cups of our to make each cupcake while a cake takes two cups of our and the baker is making 25 cupcakes and four round cakes an inequality could be used to determine how much our is needed to fill the customer s order If we added the that the baker has 9 cups of our we could use an inequality to figure out if there is or is not enough our to complete the order and if not how much more would be needed Ozark Furniture specializes in making rocking chairs They make both classic and modern rocking chairs which require the same type of maple lumber For the company it is important to know how many of each chair they can make with the amount of lumber they have on hand Ozark uses 15 board feet of maple lumber for each classic rocking chair and 12 board feet of maple lumber for their modern rocking chairs The most the company can obtain up to 3000 board feet of maple lumber at one time Dugopolski 2012 p 240 Using an inequality we can determine how the possible number of maple rockers both modern and classic can be made with the given amount of lumber the company has on hand TWO VARIABLE 3 To figure out how many rockers can be made we begin by defining the variable The feet of maple lumber for each classic rocking chair will be represented with c and the feet of maple lumber for the modern rocking chairs will be represented with m Since each classic rocking TwoVariable Inequality chair requires 15 feet of maple lumber the expression representing the multiplication will be 15c and since each modern rocker requires 12 feet of lumber 12m will be used The total amount of lumber that can be housed at the furniture store is limited to 3000 board feet Since we know that the 3000 board feet of lumber is all the company can use 3000 must be included in the solution set so less than or equal to will be used in the inequality The inequality showing the relationship between the variables and total board feet is 15c 12m S 3000 If e is on the horizontal axis as the independent variable and m is the dependent variable on the vertical axis then the inequality can be graphed using the intercepts of an equation If 0 is substituted for a variable then we can solve for the other using equation steps The cintercept is found when m 0 15c S 3000 c S 200 The cintercept is 200 0 The mintercept is found when c 0 12m S 3000 m S 250 The mintercept is 0 250 TWO VARIABLE 4 This is a less than or equal to inequality so the line will be solid sloping downward as it moves from left to right The shaded section will be from the line towards the origin and stops at the two axes To determine how many rockers can be made with 3000 feet of lumber the company has in house we can use TwoVariable Inequality 12015 5012 3000 feet of maple lumber This means that the company can make 120 classic rocking chairs and 50 modern rocking chairs at one time if graphed 120 50 would appear inside of the shaded region On the other hand 20015 8012 3324 feet of maple lumber This means that the company would have to make 180 classic rocking chairs and 52 modern rocking chairs at one time but this would not be possible because they would not have enough lumber to make both types of rockers They would need an addition 324 feet of lumber to complete all of the rockers requested If Ozark receives an order from a furniture store for 175 modern rocking chairs and 125 classic rocking chairs It will take 117 feet of lumber to make one modern rocker so it will take 20475 feet of lumber to make 175 modern rocking chairs and it takes 104 feet of lumber to make one classic rocking chair so to make 125 modern rocking chairs it takes a total of 1300 feet of lumber In order to complete the order the company needs 33475 feet of lumber The company does not keep enough lumber on hand to complete the request and would need an additional 3475 feet of lumber Inequality equations can be used to determine many different things They can be used to figure out if you have enough of an item or if you need more Companies can benefit from using inequalities to judge how productive they are being It is good way to cut down on production cost and increase in revenue for the company TWO VARIABLE 5 Reference Dugopolski M 2012 Elementary and intermediate algebra 4th ed New York NY MCGraWHill Publishing
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