Stat 200 week 6 homework solution correct answers

2. A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Each product requires 10 hours of processing time on line 1, while on line 2 products 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is $6 per unit, and the profit for product 2 is $4 per unit. a. Formulate a linear programming model for this problem. b. Solve the model by using graphical analysis. Answer: formulation: X1 = amount of product 1 X2 = amount of product 2 Maximize 6X1 + 4X2 subject to: 10X1 + 4X2 <=100 7X1 + 3X2 <= 42 X1, X2 >=0 b) I draw the feasible set which has 3 corners D(0,0), B(0,14), A(6,0) One of them is the optimal solution. Now if we check for which value 6X1 + 4X2 is maximum, if we check then we get (0,14) (i.e. X1 = 0, X2 = 14) for which 6X1 + 4X2 is maximum and the maximum value is 56. 6. The Pinewood Furniture Company produces chairs and tables from two resources – labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6 board-ft. of wood. The profit derived from each chair is $400 and from each table, $100. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit. Formulate a linear programming model for this problem. a. Formulate a linear programming model for this problem. b. Solve the model by using graphical analysis. Answer: X represents the production of chairs and Y represents the production of tables. Since profit from each chair is $400, and from each table its $100, then the objective function is 400X + 100Y. So the linear program starts with: M...

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