Solved: Write in nonnal form and solve by the simplex

Write in normal form and solve by the simplex method, assuming all \(x_{j}\) to be nonnegative. Maximize \(f=3 x_{1}+2 x_{2}\) subject to \(3 x_{1}+4 x_{2} \leqq 60, 4 x_{1}+3 x_{2} \leqq 60, \quad 10 x_{1}+2 x_{2} \leqq 120\). Text Transcription: x_j f = 3x_1 + 2x_2 3x_1 + 4x_2 leqq 60, 4x_1 + 3x_2 leqq 60, 10 x_1 + 2x_2 leqq 120

Write in normal form and solve by the simplex method, assuming all \(x_{j}\) to be nonnegative. Prob. 16 in Problem Set 22.2. Text Transcription: x_j

Write in normal form and solve by the simplex method, assuming all \(x_{j}\) to be nonnegative. Maximize the profit in the daily production of \(x_{1}\) metal frames \(F_{1}\) ($90 profit/frame) and \(x_{2}\) frames \(F_{2}\) ($50 profit/frame) under the restrictions \(x_{1}+3 x_{2} \leqq 1800\) (material), \(x_{1}+x_{2} \leqq 1000\) (machine hours), \(3 x_{1}+x_{2} \leqq 2400\) (labor). Text Transcription: x_j x_1 F_1 x_2 F_2 x_1 + 3x_2 leqq 1800 x_1 + x_2 leqq 1000 3x_1 + x_2 leqq 2400

Write in normal form and solve by the simplex method, assuming all \(x_{j}\) to be nonnegative. Maximize \(f=2 x_{1}+3 x_{2}+x_{3}\) subject to \(x_{1}+x_{2}+x_{3} \leqq 4.8,10 x_{1}+x_{3} \leqq 9.9, x_{2}-x_{3} \leqq 0.2\). Text Transcription: x_j f = 2x_1 + 3x_2 + x_3 x_1 + x_2 + x_3 leqq 4.8,10 x_1 + x_3 leqq 9.9, x_2 - x_3 leqq 0.2

Write in normal form and solve by the simplex method, assuming all \(x_{j}\) to be nonnegative. The problem in the text with the order of the constraints interchanged. Text Transcription: x_j

Write in normal form and solve by the simplex method, assuming all \(x_{j}\) to be nonnegative. Minimize \(f=4 x_{1}-10 x_{2}-20 x_{3}\) subject to \(3 x_{1}+4 x_{2}+5 x_{3} \leqq 60, \quad 2 x_{1}+x_{2} \leqq 20\) \(2 x_{1}+3 x_{3} \leqq 30\) Text Transcription: x_j f = 4x_1 - 10x_2 - 20x_3 3x_1 + 4x_2 + 5x_3 leqq 60, 2x_1 + x_2 leqq 20 2x_1 + 3x_3 leqq 30

Write in normal form and solve by the simplex method, assuming all \(x_{j}\) to be nonnegative. Minimize (f=5 x_{1}-20 x_{2}\) subject to \(-2 x_{1}+10 x_{2} \leqq 5\), \(2 x_{1}+5 x_{2} \leqq 10\) Text Transcription: x_j f = 5x_1 - 20x_2 -2x_1 + 10x_2 2x_1 + 5x_2 leqq 10

Write in normal form and solve by the simplex method, assuming all \(x_{j}\) to be nonnegative. Prob. 20 in Problem Set 22.2. Text Transcription: x_j

Write in normal form and solve by the simplex method, assuming all \(x_{j}\) to be nonnegative. Maximize \(f=34 x_{1}+29 x_{2}+32 x_{3}\) subject to \(8 x_{1}+2 x_{2}+x_{3} \leqq 54,3 x_{1}+8 x_{2}+2 x_{3} \leqq 59\), \(x_{1}+x_{2}+5 x_{3} \leqq 39\). Text Transcription: x_j f = 34x_1 + 29x_2 + 32x_3 8x_1 + 2x_2 + x_3 leqq 54, 3x_1 + 8x_2 + 2x_3 leqq 59 x_1 + x_2 + 5x_3 leqq 39

Simplex Method. (a) Write a program for graphing a region R in the first quadrant of the \(x_{1} x_{2}\)-plane determined by linear constraints. (b) Write a program for maximizing \(z=a_{1} x_{1}+c_{2} x_{2}\) in R. (c) Write a program for maximizing \(z=a_{1} x_{1}+\cdots+a_{n} x_{n}\) subject to linear constraints. (d) Apply your programs to problems in this problem set and the previous one. Text Transcription: x_{1} x_{2} z = a_{1} x_{1} + c_{2} x_{2} z = a_{1} x_{1} + cdots +a_{n} x_{n}