Problem 4 General Dynamics Land Systems produces a wide variety of vehicles. Next year they plan to focus heavily on submarines, destroyers, light armored vehicles, and gulf- stream jets. General Dynamics is concerned about production because they have a limited amount of steel, plastic, and rubber that each vehicle requires. They plan on acquiring 16 million pounds of steal, 20 million pounds of plastic, and 13.6 million pounds of rubber. To help determine an optimal production strategy, representatives from the company formulate the following linear program. max s.t. The number of submarines, destroyers, light armored vehicles, and gulfstream jets manufac- tured are represented by , 22, 23 and 24, respectively, with a profit associated with each vehicle of $100 million, $32 million, $28 million, and $30 million, respectively. When solving the model, the company obtains the following tableau. B.V. Z x2 I3 100x1+32x2+28x3 + 30x4 32x1 + 4x2 + 4x3 + 10x4 16000 (Steel) 10x + 6x2 + 4x3+4x4 20000 (Plastic) 8x1 +4x2+2.4x3 + 2x4 13600 (Rubber) T1, T2, T3, T420 x7 x1 x2 x4 80 0 28 -11 1 0 -3 19 0 1 6.4 0 0 I3 0 X5 5 -0.5 5.5 0.75 0.8 0.2 x6 I7 2 0 0.5 0 -0.5 0 -0.8 1 RHS 120000 2000 2000 800 Problem 4 cont. (a) What is the optimal solution, and what is the optimal solution value? (b) If you had to decided between acquiring additional steel, plastic, or rubber which would you chose and why? (c) By how much should the profit of gulfstream jets change so that they are produced in an optimal solution? (d) What should the minimum profit of light armored vehicles be so that the company continues to produce them? (e) Representatives from the company are concerned their production plan is highly sen- sitive to the actual amount of plastic they are able to obtain, and deviating from the planned 20 million pounds will cause them to drastically change their plan by manufacturing a different mixture of vehicles. What can you say in response to their concerns? (f) A brand new supplier approaches the company and offers to sell them an additional 500,000 pounds of plastic at a price of $1.75 million per thousand pounds. How should General Dynamics respond to this offer?