I am having trouble figuring out the equations for this problem. I think that I am reading too much into it.

As a business owner there are many decisions that you need to make on a daily basis, such as ensuring you reach the highest production levels possible with your company’s products. Your company produces two models of bicycles: Model A and Model B. Model A takes 2 hours to assemble, where Model B takes 3 hours to assemble. Model A costs $25 to make per bike where Model B costs $30 to make per bike. If your company has a total of 34 hours and $350 available per day for these two models, how many of each model can be made in a day?

* Solve the equations for the different bicycle models that can be made daily with the desired technique learned (graphing, substitution, elimination, matrix).
* Explain how to check your solution for both equations.

The problem gives you two "constraints" that the manufacturer must stay within. Letting A and B denote the number of A models and B models produced each day, respectively,

... the first constraint is that no more than 34 hours can be expended on production:



... the second limitation is that the total dollars expended must be no more than $350:



Graph both of these linear inequalities, with the horizontal axis representing either A or B, and the vertical axis for the other. Since both conditions must be satisfied, your shading of the "feasibility range" will be that area that lies beneath both lines at all times.

The maximum feasible daily production will be the various combinations of As and Bs that represent the upper boundary of your shaded area. Also remember to limit your attention to Quad I of your graph, as Quads II - IV represent negative production quantities, and so should be disregarded.

Hope that helped out a bit.