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Chapter 7: Problem 91
What does a dashed line mean in the graph of an inequality?
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an objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of \(x\) and \(y\) for which the maximum occurs. Objective Function \(\quad z=3 x+2 y\) Constraints \(\left\\{\begin{array}{l}x=0, y \geq 0 \\ x+y \leq 8 \\ x+y \geq 4\end{array}\right.\)
With the current, you can canoe 24 miles in 4 hours. Against the same current, you can canoe only \(\frac{3}{4}\) of this distance in 6 hours. Find your average velocity in still water and the average velocity of the current.
A person invested \(\$ 6700\) for one year, part at \(8 \%,\) part at \(10 \%,\) and the remainder at \(12 \% .\) The total annual income from these investments was \(\$ 716 .\) The amount of money invested at \(12 \%\) was \(\$ 300\) more than the amount invested at \(8 \%\) and \(10 \%\) combined. Find the amount invested at each rate.
When using the addition or substitution method, how can you tell if a system of linear equations has no solution? What is the relationship between the graphs of the two equations?
How do you determine if an ordered pair is a solution of an inequality in two variables, \(x\) and \(y ?\)
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