Exam 7: Systems Of Equations and Inequalities

Find the maximum value of the objective function and where it occurs, subject to the constraints: Objective function: Z = 5x + y Constraints: X $\ge$ 0 Y $\ge$ 0 X + 4y $\le$ 20 X + y $\le$ 18 2x + 2y $\le$ 21

Write the partial fraction decomposition of the rational expression. $\frac { - 3 x ^ { 2 } - 3 x + 27 } { x ^ { 2 } ( x + 3 ) }$

Select the correct graph of the inequality. $y < 4 - x$

Find the equilibrium point (x,p) of the demand and supply equations.The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations. Demand Supply p=140-0.00003x p=90+0.00001x

The linear programming problem has an unusual characteristic.Select a graph of the solution region for the problem and describe the unusual characteristic.Find the minimum and maximum value of the objective function (if possible) and where it occurs. ​ Z = x + y ​ Constraints: ​ X ≥ 0 Y ≥ 0 -x + y ≤ 0 -5x + y ≥ 5 ​

Solve the system by substitution, if possible. $\left\{ \begin{array} { l } y = 7 x - 21 \\9 x - y = 29\end{array} \right.$

Use any method to solve the system of linear equations, find (x,y). $\left\{ \begin{array} { l } y = - 7 x - 12 \\y = 7 - 8 x\end{array} \right.$

Find the equilibrium point (x,p) of the demand and supply equations.The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations. Demand Supply p=570-0.5x p=370+0.3x

Write the partial fraction decomposition of the rational expression. $\frac { x ^ { 2 } } { x ^ { 4 } - 23 x ^ { 2 } - 50 }$

Write the partial fraction decomposition of the rational expression. $\frac { 1 } { y ( q - y ) }$

The total weekly sales for a newly released portable media player (PMP) increased each week.At the same time, the total weekly sales for another newly released PMP decreased each week.Models that approximate the total weekly sales S (in thousands of units) for each PMP are $\left\{ \begin{array} { l l } S = 10 x + 70 & \text { PMP1 } \\S = - 10 x + 210 & \text { PMP2 }\end{array} \right.$ where x represents the number of weeks each PMP was in stores, with x = 0 corresponding to the PMP sales on the day each PMP was first released in stores.After how many weeks will the sales for the two PMPs be equal

Thirty liters of a 40% acid solution is obtained by mixing a 28% solution with a 43% solution.How much of each solution is required to obtain the specified concentration of the final mixture? Use this system of linear equations there x and y represents the amounts of the 28% solution and 43% solution. $\left\{ \begin{array} { l } x + y = 30 \\0.28 x + 0.43 y = 12\end{array} \right.$

Find values of x, y, and $\lambda$ that satisfy the system.These systems arise in certain optimization problems in calculus, and $\lambda$ is called a Lagrange multiplier. $\left\{\begin{array}{ll}2 x+\lambda & =0 \\2 y+\lambda & =0 \\x+y-10 & =0\end{array}\right.$

Select a set of inequalities to describe the region.

Use a graphing utility to graph the inequality.Shade the region representing the solution. $y$ $\le$ $2 ^ { 1 - x }$

Find the sales necessary to break even (R = C) for the cost C of producing x units and the revenue R obtained by selling x units.(Round to the nearest whole unit.) $C = 6.5 \sqrt { x } + 9,674 , R = 3.2 x$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x + 2 } { x ^ { 2 } ( 3 x - 8 ) ^ { 2 } }$

During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 225 tickets and collected $1638.If adult tickets sold for $9 and children's tickets sold for $6, how many of each type of ticket were sold? ​

Write the partial fraction decomposition of the rational expression. $\frac { 1 } { 16 x ^ { 2 } - 121 }$

Find the minimum value of the objective function and where it occurs, subject to the indicated constraints. ​ Objective function: ​ Z = 4x + 7y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X + 3y ≤ 15 4x + y ≤ 16​ ​