\"Woody\'s Furniture Manufacturing\", Part II: solving algebraically In the prev
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Question
"Woody's Furniture Manufacturing", Part II: solving algebraically In the previous Class Activity, you modeled and solved the Woody's Furniture Manufac- turing problem graphically. That is, you graphed the feasible region of solutions, identified the corner points of the feasible region, and used the corner points together with the profit objective function to find the corner point that maximized profit. That corner point was (z,y) (40, 40) which yielded a maximum profit of $3, 200. That activity was based on the approach to solving linear programming problems presented in Section 5.3. In this Class Activity, you will solve the same Woody's Furniture Manufac- turing problem algebraically. This activity is based on the approach to solving linear programming problems presented in Section 6.1 Recall the Woody's Furniture Manufacturing problem: Woody's Furniture Manufacturing Company produces tables and chairs. A table requires 8 labor hours for assembling and 2 labor hours for finishing. A chair requires 2 labor hours for assembling and 1 labor hour for finishing. The maximum number of labor hours available per day are 400 hours for assembling and 120 hours for finishing. Each table produced and sold yields a $60 profit and each chair produced and sold yields a $20 profit. Let z represent the number of tables produced per day, and let y represent the number of chairs produced per day. The linear programming problem can be written as follows: Maximize Profit P 60r 20y subject to 8r 2y S 400 2r y 120 and r 20, y 2 0 (a). Convert each of the two "S" constraint inequalities to equations by introducing two new nonnegative slack variables si and s2 to the model. (b). How many basic variables will there be in a basic solution to the Woody's Furniture Manufacturing problem? Why? How many nonbasic tariables will there be in a basic solution to the Woody's Furniture Manufacturing problem? Why?Explanation / Answer
a) Standard form of the constraints:
8x+2y+s1=400
2x+y+s2=120
objective function:
maximise profit P= 60x+20y+0*s1+0*s2
The optimal solution is:
objective function P=3200
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