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Chapter 5: Problem 8
Graph each inequality. $$y>3 x+2$$
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Because \(x+5\) is linear and \(x^{2}-3 x+2\) is quadratic, I set up the following partial fraction decomposition: $$ \frac{7 x^{2}+9 x+3}{(x+5)\left(x^{2}-3 x+2\right)}=\frac{A}{x+5}+\frac{B x+C}{x^{2}-3 x+2} $$ Because \(x+5\) is linear and \(x^{2}-3 x+2\) is quadratic, I set up the following partial fraction decomposition: $$ \frac{7 x^{2}+9 x+3}{(x+5)\left(x^{2}-3 x+2\right)}=\frac{A}{x+5}+\frac{B x+C}{x^{2}-3 x+2} $$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. In order to solve a linear programming problem, I use the graph representing the constraints and the graph of the objective function.
Consider the objective function \(z=A x+B y \quad(A>0\) and \(B>0\) ) subject to the following constraints: \(2 x+3 y \leq 9, x-y \leq 2, x \geq 0,\) and \(y \geq 0 .\) Prove that the bbjective function will have the same maximum value at the vertices \((3,1)\) and \((0,3)\) if \(A=\frac{2}{3} B\)
At a college production of \(A\) Streetcar Named Desire, 400 tickets were sold. The ticket prices were 8 dollar ,10 dollar, and 12 dollar, and the total income from ticket sales was 3700 dollar. How many tickets of each type were sold if the combined number of 8 dollar and 10 dollar tickets sold was 7 times the number of 12 dollar tickets sold?
What is a constraint in a linear programming problem? How is a constraint represented?
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