Set Up and Solve Each of the Following. Include the following: A. All of the inequalities. Be sure to identify the...

Set Up and Solve Each of the Following. Include the following: A. All of the inequalities. Be sure to identify the variables. B. Identify the Objective Function C. The graph of the feasible set D. All possible solutions E. The requested response 1. An automobile manufacturer has assembly plants in Detroit and Cleveland, each of which can assemble cars and trucks. The Detroit plant can assemble at most 800 vehicles in one day at a cost of $1200/car and $2100/truck. The Cleveland plant can assemble at most 500 vehicles in one day at a cost of $1000/car and $2000/truck. A rush order is received for 600 cars and 300 trucks. How many vehicles of each type should each plant produce to fill the order at the least cost? 2. Ms. Jones installs and demonstrates smoke detectors. There are two types of smoke detectors, Type A and Type B. Type A requires 1 hour to install and 1/3 hour to demonstrate. Type B requires 1.5 hours to install and 1/5 hour to demonstrate. Company rules require Ms. Jones to work a minimum of 20 hours as an installer and a maximum of 15 hours a week as a demonstrator. She earns $8 per hour as an installer and $5 per hour as a demonstrator. How many of each type of alarm should she install and demonstrate to maximize her income?