What is the maximum profit attainable while satisfying all the constraints?

Problem 3 - Sensitivity

Martin Automotive is a smaller firm that manufactures automobiles and wants to maximize profit. They are restricted by federal regulations that limits the number of gas guzzlers they can produce. The company’s CEO, Armando, likes safe vehicles and makes the company manufacture a set minimum of 5-star crash test rated vehicles each period. Armando assembled his finance and operations departments to determine the ideal product mix to maximize profit.The company is also met by constraints on different production mixes, automobile components like headlights and transmissions, and others that you can see below.

The linear programming output and the sensitivity analysis for their maximized profit are presented below. Please note that the optimal values of the decision variables are not integer values (they do not have to be integers to answer the questions regarding sensitivity analysis).

    

Constraints Max # Gas Guzzlers Max Manual Transmission Max Auto Transmission Max Labor (hours) Max # HID Headlights Max # Traditional Headlights Max # Airbags Min # 5-Star Crash Test Min Union Labor (hours) Min # 4-Door Min # Pick-Ups or SUV's Sports Cars $12,000.00 $10,000.00 1 1 20 4 9 Pick-ups 6 1 1 18 2 2 14 1 5 1 1 SUV's $9,000.00 1 1 16 4 16 1 5 1 1 Crossovers Sedans $6,000.00 $3,000.00 1 15 2 10 1 4 1 1 14 2 7 1 5 1 Coups ($1,200.00) 1 8 2 6 10 2,437.5 1,375.0 2,000.0 50,000.0 8,000.0 3,625.0 39,812.5 2,000.0 22,000.0 2,000.0 2,000.0 3,000 3,000 4,500 50,000 8,000 6,500 42,000 2,000 22,000 800 1,000