* SOLVING LINEAR PROGRAMMING PROBLEMS GRAPHICALLY: A furniture company sells two types of patio chairs. The company makes a profit of $176 dollars on the chair with arms(Style A) and a profit of $92 dollars on the chair without arms(Style B). The armed chair requires 2 hours to cut the materials, 4 hours to finish the chair, and 1 hour to package. The armless chair requires 1 hour to cut materials, 3 hours to finish the chair, and 1 hour to package. The company has a maximum of 200 labor hours available for cutting materials, a maximum of 480 hours of labor available in the finishing department and a maximum of 150 labor hours available in the packaging department. How many of each style of chair should be produced and sold in order for the company to maximize its profit?

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Asked Dec 5, 2019
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* SOLVING LINEAR PROGRAMMING PROBLEMS GRAPHICALLY:

 

A furniture company sells two types of patio chairs. The company makes a profit of $176 dollars on the chair with arms(Style A) and a profit of $92 dollars on the chair without arms(Style B). The armed chair requires 2 hours to cut the materials, 4 hours to finish the chair, and 1 hour to package. The armless chair requires 1 hour to cut materials, 3 hours to finish the chair, and 1 hour to package. The company has a maximum of 200 labor hours available for cutting materials, a maximum of 480 hours of labor available in the finishing department and a maximum of 150 labor hours available in the packaging department. How many of each style of chair should be produced and sold in order for the company to maximize its profit?

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The objective function or profit function becomes P(x, y) =176x+92y as a profit of $176 dollars on the chair with arms (Style A) and a profit of $92 dollars on the chair without arms (Style B) is made. The constraint related to labor hours available for cutting materials becomes 2x+ y< 200 as the armed chair requires 2 hours for cutting the materials and the armless chair requires 1 hour for cutting materials. Also, the company has a maximum of 200 labor hours available for cutting materials The constraint related to labor hours available for finishing materials becomes 4x +3y <480 as the armed chair requires 4 hours to finish the chair and armless requires 3 hours to finish the chair. Also, the company has a maximum of 480 labor hours available for finishing materials The constraint related to labor hours available for packaging materials becomes x+ y s150 as the armed chair requires 1 hour for packing the chair and the armless requires 1 hour for packing the chair. Also, the company has a maximum of 150 labor hours available for packaging materials.

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200 150 (0, 150) 30, 120) 100- Y60, 80) 50- (100, 0)00 150 The corner points of the feasible region are (0,150).(30,120).(60,80) and (100,0).

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P =176x +92 y (x,y) P=176(0)+92(150) = $13800 P=176(30)+92(120) = $16320 (0,150) (30,120) (60, 80) (100,0) P =176(60)+92(80)=$17680 P =176(100)+92(0) = $17600 Thus, the maximum profit occurs at the point (60,80), that is x= 60 and y = 80 .

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