The History Of The Ozark Furniture Company

Published Date: 02 Nov 2017

Kamara Week Aminata III Assignment 10/27/12 Q. Ozark Furniture Company can obtain at most 3000 board feet of maple lumber for making its classic and modern maple rocking chairs. A classic maple rocker requires 15 board feet of maple, and a modern rocker requires 12 board feet of maple. Write an inequality that limits the possible number of maple rockers of each type that can be made, and graph the inequality in the first quadrant. After reading the above problem on page 240 of Elementary and Intermediate Algebra, my assign variable to each type of rocker Ozark Furniture is as follows Let c = the number of classic rocker Let m = the number of modern rocker Each classic rocker requires 15 board feet of maple lumber, and modern rocker requires 12 board feet of lumber. The total amount of maple lumber which can be used is 3000 board feet. My inequality looks like this: 15c + 12m 3000 =12m3000-15c moving 15c to the right side of the inequality and I subtract 15c from both sides =12m/123000/12-15c/12 removing the common factors = m250-15c/12 I call c independent the variable on the horizontal axis and m the dependent variable on the vertical axis I graph the equation using the intercepts. The c-intercept is found when m = 0 and solve for c 15c 3000 =c 200 the c-intercept is (200, 0). The m-intercept is found when c = 0 and solve for m 12m 3000 =m 250 the m-intercept is (0, 250). The inequality is a less than or equal to so the feasibility will be at or below the graph line, sloping downward as it moves from left to right. The region of the graph which is relevant to this problem is restricted to the first quadrant, so the shaded section is from the line towards the origin and stops at the two axes. The point of my graph is outside the shaded area which means that Ozark Furniture could not fill the chain furniture store order of 175 modern rocking chairs and 125 classic rocking, if they made up this many items they would go over the limit board feet of maple lumber requires. 175(115) + 125(12) = 4125 board feet of maple lumber and they will have to used 1125 board feet of maple lumber more.

Ozark Furniture Company can obtain at most 3000 board feet of maple lumber for making its classic and modern maple rocking chairs. A classic maple rocker requires 15 board feet of maple, and a modern rocker requires 12 board feet of maple. Write an inequality that limits the possible number of maple rockers of each type that can be made, and graph the inequality in the first quadrant.

Let x = no. of classics

Let y - no. of moderns

:

15x + 12y =< 3000

:

12y =< -15x + 3000

:

y =< -(15/12)x + 3000/12

:

y = -1.25x + 250; graph this equation from x=0 to x=200

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Graph should look like this:

+graph%28+300%2C+200%2C+-20%2C+260%2C+-20%2C+300%2C+-1.25x+%2B+250%29+

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Area of feasibility will be at or below that graph line

:

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After {reading|looking at} the above {problem|situation} on {page|article} 240 of Elementary and Intermediate Algebra, my {assign|connect} variable to {each|the two} {type of|style of} rocker Ozark Furniture {is as|will be as} follows {Let|Make} c = the {number of|numbers of} classic rocker Let m = the number of modern rocker {Each|The} classic rocker {requires|needs} 15 board feet of maple lumber, {and|together with} modern rocker {requires|needs to have} 12 board feet of lumber. The total amount of maple lumber {which can be used|that are available} is 3000 board feet. My inequality {looks like|seems like} this: 15c + 12m 3000 =12m3000-15c {moving|relocating} 15c to the right side of the inequality {and|then} I subtract 15c from {both sides|each side} =12m/123000/12-15c/12 {removing|getting rid of} the common factors = m250-15c/12 I call c independent the variable on the horizontal axis {and|and then|while} m the dependent variable on the vertical axis I graph the equation {using|by making use of} the intercepts. The c-intercept {is found|can be located} {when|once} m = 0 and {solve|find the solution to} for c 15c 3000 =c 200 the c-intercept is (200, 0). The m-intercept {is found|can be located|can be obtained} {when|whenever} c = 0 and {solve|find the solution to} for m 12m 3000 =m 250 the m-intercept is (0, 250). The inequality is a less than or equal to {so|as a result} the feasibility {will be|should be} at {or|or perhaps} below the graph line, sloping {downward|downwards} {as it|because it} {moves|goes} from left to right. The {region|regional} of the graph which is relevant to this problem is restricted to the first quadrant, {so|therefore|as a result} the {shaded|shady} {section|sector} is from the line {towards|in the direction of} the {origin|inception} {and|then} {stops|stop} at the two axes. The point of my graph is outside the shaded area which means that Ozark Furniture could not fill the chain furniture store order of 175 modern rocking chairs and 125 classic rocking, if they made up this many items they would go over the limit board feet of maple lumber requires. 175(115) + 125(12) = 4125 board feet of maple lumber and they will have to used 1125 board feet of maple lumber more.