Exam 46: Linear Programming

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

Find the minimum value of the objective function and where it occurs,subject to the indicated constraints. ​ Objective function: ​ Z = 10x + 4y ​ Constraints: ​ 0 ≤ x ≤ 60 0 ≤ y ≤ 45 5x + 6y ≤ 420 ​​ ​

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 = 5x + 6y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X + y ≥ 8 3x + 5y ≥ 30 ​

Find the minimum value of the objective function and where it occurs,subject to the indicated constraints. ​ Objective function: ​ Z = 5x + 4y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X + y ≤ 5​ ​​ ​

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 maximum value of the objective function (if possible)and where it occurs. ​ Z = 3x + 4y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X + y ≤1 3x + y ≤ 6 ​

According to automobile association of a country,on March 27,2009,the national average price per gallon of regular unleaded (86-octane)gasoline was $2.02,and the price of premium unleaded (91-octane)gasoline was $2.26.The cost of the blend of mid-grade unleaded gasoline (90-octane).Select a graph of the region determined by the constraints. ​ Constraints: ​ X ≥ 0 Y ≥ 0 X + y = 1 86x + 91y = 90 ​

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:? $z = 7 x + \frac { 1 } { 4 } y$ ? Constraints:? x \geq0 y \geq0 x+y \leq8 x+y \geq4 ?

An accounting firm has 780 hours of staff time and 272 hours of reviewing time available each week.The firm charges $1000 for an audit and $350 for a tax return.Each audit requires 60 hours of staff time and 16 hours of review time.Each tax return requires 10 hours of staff time and 4 hours of review time.What numbers of audits and tax returns will yield an optimal revenue? What is the optimal revenue? ​

An investor has $450,000 to invest in two types of investments.Type A pays 6% annually and type B pays 7% annually.To have a well-balanced portfolio,the investor imposes the following conditions.At least one-third of the total portfolio is to be allocated to type A investments and at least one-third of the portfolio is to be allocated to type B investments.What is the optimal amount that should be invested in each investment?

Find the maximum value of the objective function and where it occurs,subject to the indicated constraints. ​ Objective function: ​ Z = 9x + 5y ​ Constraints: ​ 0 ≤ x ≤ 60 0 ≤ y ≤ 45 5x + 6y ≤ 420​ ​

Find the maximum value of the objective function and where it occurs,subject to the indicated constraints. ​ Objective function: ​ Z = 4x + 5y ​ Constraints: ​ X ≥ 0 ​3x - y ≤ 9 2x + 3y ≥ 6 X + 4y ≤ 16 ​​ ​

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 + 2y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X ≤ 10 X + y ≤ 8 ​

Find the maximum value of the objective function and where it occurs,subject to the indicated constraints. ​ Objective function: ​ ​ Z = 5x + 8y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X + 3y ≤ 15 4x + y ≤ 16 ​​ ​

Select the region determined by the constraints.Then find the maximum value of the objective function (if possible)and where it occurs,subject to the indicated constraints. ? Objective function:? $z = 7 x + \frac { 1 } { 8 } y$ ? Constraints:? x \geq0 y \geq0 x+y \leq8 x+y \geq4 ?

Select the region determined by the constraints.Then find the maximum value of the objective function (if possible)and where it occurs,subject to the indicated constraints. ​ Objective function: ​ Z = 8x + 7y ​ Constraints: ​ X ≥ 0 Y ≥ 0 2x + 2y ≥ 10 X + 2y ≥ 6 ​

According to automobile association of a country,on March 27,2009,the national average price per gallon of regular unleaded (88-octane)gasoline was $2.08,and the price of premium unleaded (93-octane)gasoline was $2.27.Write an objective function that models the cost of the blend of mid-grade unleaded gasoline (89-octane).What is the optimal cost? ​

Select the region determined by the constraints.Then find the maximum value of the objective function (if possible)and where it occurs,subject to the indicated constraints. ​ Objective function: ​ Z = 8x + 9y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X + y ≥ 8 3x + 5y ≥ 30 ​

According to automobile association of a country,on March 27,2009,the national average price per gallon of regular unleaded (85-octane)gasoline was $2.02,and the price of premium unleaded (93-octane)gasoline was $2.23.The cost of the blend of mid-grade unleaded gasoline (92-octane).Determine the constraints for the objective function. ​

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 + y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X + y ≤ 1 3x + y ≤ 6 ​

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​ ​