He earns $25 per hour for training and $15 per hour for data entry support. Steven can work no more than 40 hours a week. He wan
ts to use linear programming techniques to optimize his income. Part A Construct a model to represent the amount of time Steven can spend on data entry and training. Be sure to define your variables. Sketch a graph of your model. Part B While Steven would like to spend most of his time training, the number of hours spent training cannot exceed twice the number of hours doing data entry support. Steven must spend at least 10 hours each week on data support. Construct a model to show the constraints. Sketch a graph of your model. Part C Find the vertices of the feasible region. Show your work or explain how you found the coordinates. Part D What is the maximum possible amount of money Steven can earn in a week given the constraints? Round to the nearest dollar. Validate your solution to assess the reasonableness of you Part E The number of hours Steven worked one week resulted in a gross income of $800. From this, a portion was withheld for benefits, retirement, and taxes. The total amount withheld from Steven’s check was $264. The amount withheld for taxes was twice the amount withheld for retirement, and the amount withheld for benefits was $24 less than the sum of retirement and taxes. Construct a system of equations that can be used to find the amount of benefits, retirement, and taxes. Be sure to define your variables. Part F Solve the system from Part E. Validate your solution to assess the reasonableness of your model.
Please see below solution: Let x = number of books that Bryan reads2x for amanda = Amanda 3x - 4 for Colin Amanda = 5/8(Bryan + Colin)2x = 5/8(x+3x-4)2x = 5/8(4x-4)
[16x = 5(4x-4)]816x = 20x - 20Subtract 20x from each side-4x =-20-4x/-4= -20/-4 divide -4 to eliminate the -4 in -4xx = 5 Therefore: Bryan reads 5 books a month. Since Amanda reads twice as many books a Bryan read so Amanda 10 books a month. And Colin 11 books a month. 3(5) - 4 = 11
