Exam 46: Linear Programming

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

An accounting firm has 780 hours of staff time and 272 hours of reviewing time available each week.The firm charges $1700 for an audit and $410 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? ​

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

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 = 3x + 2y ​ Constraints: ​ X ≥ 0 ​y ≥ 0 5x + 2y ≤ 20 5x + y ≥ 10 ​ ​

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. ​ Objective function: ​ ​ Z = -x + 3y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X ≤ 10 X + y ≤ 7 ​

A manufacturer produces two models of elliptical cross-training exercise machines. The times for assembling,finishing,and packaging model X are 3 hours,3 hours,and 0.8 hour,respectively.The times for model Y are 4 hours,2.5 hours,and 0.4 hour.The total times available for assembling,finishing,and packaging are 6000 hours,4200 hours,and 950 hours,respectively.The profits per unit are $200 for model X and $275 for model Y.What is the optimal production level for each model? What is the optimal profit? ​

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 ​

According to automobile association of a country,on March 27,2009,the national average price per gallon of regular unleaded (87-octane)gasoline was $2.07,and the price of premium unleaded (90-octane)gasoline was $2.25.Write an objective function that models the cost of the blend of mid-grade unleaded gasoline (89-octane). ​

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. ​ Objective function: ​ Z = x + y ​ Constraints: ​ X ≥ 0 Y ≥ 0 -x + y ≤ 1 -x + 5y ≤ 7 ​

Find the minimum 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 ​​ ​