Exam 46: Linear Programming

Find the minimum value of the objective function and where it occurs,subject to the constraints: ? Objective function: ? Z = x + 4y ? Constraints: ? X ? 0 Y ? 0 X + 4y ? 20 X + y ? 18 ?2x + 2y ? 21

Find the maximum value of the objective function and where it occurs,subject to the indicated constraints. ​ Objective function: ​ Z = 2x + 8y ​ Constraints: ​ X ≥ 0 Y ≥ 0 2x + y ≤ 12​ ​

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 value of the objective function (if possible)and where it occurs. ​ Objective function: ​ Z = x + y ​ Constraints: ​ X ≥ 0 Y ≥ 0 -x + y ≤ 1 -x + 5y ≤ 7 ​

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

Select the region determined by the constraints.Then find the minimum value of the objective function (if possible)and where it occurs,subject to the indicated constraints. ​ Objective function: ​ Z = 7x + 6y ​ Constraints: ​ X ≥ 0 ​y ≥ 0 5x + 2y ≤ 20 5x + y ≥ 10 ​

A merchant plans to sell two models of MP3 players at prices of $225 and $250.The $225 model yields a profit of $30 per unit and the $250 model yields a profit of $31 per unit.The merchant estimates that the total monthly demand will not exceed 280units.The merchant does not want to invest more than $55,776 in inventory for these products.What is the optimal inventory level for each model? What is the optimal profit? ​

Find the minimum and maximum values of the objective function and where it occurs,subject to the indicated constraints. Objective function: Z = 3x + 4y Constraints: $\left\{ \begin{array} { l } y \geq 0 \\x - y \geq - 2 \\2 x + 3 y \geq 6 \\5 x + 2 y \leq 25\end{array} \right.$ ?

Find the maximum value of the objective function and where it occurs,subject to the constraints: ? Objective function: ? Z = 8x + 9y ? Constraints: ? X ? 0 Y ? 0 X + 4y ? 20 X + y ? 18 ?2x + 2y ? 21 ?

An animal shelter mixes two brands of dog food.Brand X costs $29 per bag and contains two units of nutritional element A,two units of element B,and two units of element C.Brand Y costs $22 per bag and contains one unit of nutritional element A,nine units of element B,and three units of element C.The minimum required amounts of nutrients A,B,and C are 12 units,36 units,and 24 units,respectively.What is the optimal number of bags of each brand that should be mixed? What is the optimal cost? ​

Find the maximum value of the objective function and where it occurs,subject to the indicated constraints.(You should graph the feasible solutions on the grid below before you attempt to find the minimum and maximum values. ) Objective function: Z = 6x - 7y Constraints: $\left\{ \begin{array} { l } x \geq 0 \\y \geq 0 \\5 x + 4 y \leq 20 \\3 x + 2 y \leq 6\end{array} \right.$

Find the maximum value of the objective function and where it occurs,subject to the constraints: ? Objective function: ? Z = 12x + 24y ? Constraints: ? X ? 0 Y ? 0 X + 4y ? 20 X + y ? 18 ?2x + 2y ? 21 ?

Select the region determined by the constraints.Then find the minimum value of the objective function (if possible)and where it occurs,subject to the indicated constraints. ​ Objective function: ​ Z = 9x + 8y ​ Constraints: ​ X ≥ 0 Y ≥ 0 2x + 2y ≥ 10 X + 2y ≥ 6 ​

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

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 value of the objective function (if possible)and where it occurs. ​ Z = x + 3y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X + 2y ≤ 4 2x + y ≤ 4 ​

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 value of the objective function (if possible)and where it occurs. ? Objective function: ? Z = 2.5x + y ? Constraints: ? X ? 0 Y ? 0 3x + 5y ? 15 ?5x + 2y ? 10 ?

A humanitarian agency can use two models of vehicles for a refugee rescue mission.Each model A vehicle costs $1000 and each model B vehicle costs $1500.Mission strategies and objectives indicate the following constraints.A total of at least 20 vehicles must be used.A model A vehicle can hold 45 boxes of supplies.A model B vehicle can hold 24 boxes of supplies.The agency must deliver at least 690 boxes of supplies to the refugee camp.A model A vehicle can hold 17 refugees.A model B vehicle can hold 35 refugees.The agency must rescue at least 520 refugees.What is the optimal number of vehicles of each model that should be used? What is the optimal cost? ​

Find the minimum value of the objective function and where it occurs,subject to the indicated constraints. ​ Objective function: ​ Z = 4x + 16y ​ Constraints: ​ X ≥ 0 Y ≥ 0 2x + y ≤ 12​ ​

Find the minimum value of the objective function and where it occurs,subject to the constraints: ? Objective function: ? Z = 5x + 6y ? Constraints: ? X ? 0 Y ? 0 X + 4y ? 20 X + y ? 18 ?2x + 2y ? 21 ?

Find the maximum value of the objective function and where it occurs,subject to the constraints: ​ Objective function: ​ Z = 7x + y ​ Constraints: ​ X ≥ 0 Y ≥ 0 3x + y ≤ 15 4x + 3y ≤ 30 ​

Find the minimum value of the objective function and where it occurs,subject to the constraints: ? Objective function: ? Z = 4x + 16y ? Constraints: ? X ? 0 Y ? 0 X + 4y ? 20 X + y ? 18 ?2x + 2y ? 21 ?