Reference no: EM133023546

A company makes two models of cars, called the Avalon and the Bonavista models. After deducting all direct costs, each Avalon car gives a profit of $1020, while each Bonavista car gives a profit of $360. There is a contractual obligation to produce at least 25 Avalon cars per week. Every car goes through three assembly-lines. Every Avalon car takes 50 minutes in Assembly-line 1, 90 minutes in Assembly-line 2, and 25 minutes in Assembly-line 3. Every Bonavista car takes 40 minutes in Assembly-line 1, 45 minutes in Assembly-line 2, and 75 minutes in Assembly-line 3. Every week, Assembly-lines 1, 2, and 3 are open 80, 108, and 100 hours respectively. They want the production of Avalon cars to be no more than 80% of the total production.

(a) Formulate a linear optimization model for this situation. Write every constraint in standard form (≤, = , or ≥ a number), with a one or two word description of the purpose of the constraint.

(b) Without plotting any points outside the 150 by 150 region on the graph paper found on page 4, solve the model, clearly indicating each constraint with a word description next to it, the feasible region, the trial and optimal isovalue lines, and the point of optimality. Compute the exact solution algebraically, and clearly state the recommendation and the OFV.