Question 617649
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If you have 900 square meters of space and each bus takes 30 square meters, then the maximum number of busses you can park in the space is 30.  Hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ b\ \leq\ 30]


If you have 900 square meters of space and each car takes 6 square meters, then the maximum number of busses you can park in the space is 150.  Hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ c\ \leq\ 150]


If the maximum number of vehicles the attendant can handle is 70,


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ b\ +\ c\ \leq\ 70]


Since you can't have a negative number of vehicles of either type:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ b\ \geq\ 0]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ c\ \geq\ 0]


On a set of coordinate axes labeled *[tex \Large b] and *[tex \Large c] (doesn't really matter which axis is which) graph all of the above inequalities.  The solution set to the system of inequalities will be a quadrilateral in the first quadrant and this is your area of feasibility.  HINT:  Ordinarily when you graph an inequality, you shade in the half-plane that represents the solution set.  However, when I graph a feasibiltiy area, I generally graph the inequalities with the OPPOSITE sense.  The end result is that the feasibility area is totally unshaded and therefore much easier to differentiate from those parts of the plane that are not in the feasibility area.


I do complete linear programming optimization problems, complete with graphs and step by step explanations for $5 to $10 per problem depending on complexity.  Write back and attach your problems for a quote.


Since you make $35 per day from each car and $30 per day from each bus, your revenue (and the objective function) is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ O(c,b)\ =\ 35c\ +\ 30b]


The optimum point to maximize your objective function is either one of the vertices of the feasibility polygon or in the event that two vertices give the same objective value, any point on that edge of the polygon is optimum.


Find the coordinates of each of the vertices of the feasibility polygon and evaluate the objective function for those values.  Find the point that gives you the largest value for the objective function.


Repeat the process with the revised objective function:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ O(c,b)\ =\ 27c\ +\ 25b]


Are you sure you have the prices for cars and busses in the right order?  The way you have it, the outcome is not very interesting.  It also doesn't make much sense that you would charge less to park a vehicle that takes up 5 times the space.


I do complete linear programming optimization problems, complete with graphs and step by step explanations for $5 to $10 per problem depending on complexity.  Write back and attach your problems for a quote.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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