MA 114 Exam 2 Form B Solutions.pdf - MA 114 Introduction to...

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MA 114 - Introduction to Finite Mathematics Spring 2017 Instructor : Lucas Castle Exam 2 - Form B Solutions 1. ( Use the graphical method for the following problem ): An automobile manufacturers makes sedans and sports-utility vehicles (SUVs). The following table gives the labor requirements and prof- its per automobile: Sedans SUVS Assemble 8 labor-hours 16 labor-hours Paint 2 labor-hours 1 labor-hours Profit $90 $110 Each day, 400 labor-hours are available to assemble, 40 labor-labor hours to paint. The manufac- turer wants to determine how many vehicles to produce of each type in order to maximize profit. (a) [7 points] Define decision variables, and write down the objective function.
(b) [8 points] Identify the constraints of the problem (there are 4).
2 x + y 40 . These inequalities arise due to limitations on labor-hours. We also have the ”obvious” restric- tions x 0 and y 0. Putting everything together, we obtain 8 x + 16 y 400 2 x + y 40 x 0 , y 0 . (c) [5 points] Sketch the feasible set.

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