Ismael A. answered • 11/11/16

Tutor

New to Wyzant
Your Qualified and Motivated Math and Spanish tutor.

1) The objective function is the total profit P= the profit by selling playgrounds + the profit by selling playhouses.

Let x = number of playgrounds and y = number of playhouses.

Every time a playground is sold the company makes $100 profit. So Hanna should figure it out what happens if the company sells x playgrounds.

Every time a playhouse is sold the company makes $75 profit. So Hanna should figure it out what happens if the company sells y playhouses.

2) The constraints mean what makes sense physically in the problem context: profit is obtained from finished goods, not from unfinished goods. The company cannot sell 2.3 playgrounds but it can sell 2 (0.3 playground is an unfinished playground at some production stage, maybe drilling). Also Hanna has to consider that workers are not allowed to work more than 8 hours. The constraints translate into algebraic inequalities.

So the constraints for x would be: each x unit requires 3 hours of labor. So Hanna should figure it out the inequality for x taking into account that workers cannot work more than 8 hours.

The constraints for y: each y unit requires 2.5 hours of labor. So Hanna should figure it out the inequality for y taking into account that workers cannot work more than 8 hours.

Another constraint is that x and y has to be equal or greater than zero (it makes no sense to produce negative playgrounds or negative playhouses).

3) In this case the feasible region is a rectangular region. Hanna should figure it out how to draw it from the constraints obtained at step 2 above.

4) The vertices or corner points of the feasible region you get them from step 3.

5) There is a Theorem that says that the objective function is maximized at one of the corner points so Hanna has to try 4 corner points in this case one of which is going to give zero profit (when x=0 and y=0). Some other corners will have a decimal so Hanna will have to round them to the closest integer that is inside the feasible region.

Another way of solving this problem (not using the linear programming method) is by trying all meaningful possible (x,y) pairs in the objective function and pick the pair which maximizes the objective function. A hint: (15,4) is not possible but (1,2) is possible or meaningful.