Question 640035
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Constraints are inequalities, not equations.  Furthermore, given the cost data provided and the fact that you can't buy fractional parts of either CDs or books, there is no combination of $13 items and $55 items that total $400 -- which is simply more evidence that this should be an inequality rather than an equation.


What would have been appropriate is to ask you to write the equation, in slope-intercept form, that represents the <i><b>boundary line</b></i> of the budget constraint inequality solution set half-plane.  Such an equation would have the form *[tex \LARGE y\ =\ mx\ +\ b]


If *[tex \LARGE x] represents the number of books purchased, then the total cost of those $55 books is *[tex \LARGE 55x].  Likewise the total cost of the CDs purchased is *[tex \LARGE 13y].


Then, since the budget is $400, meaning that you cannot spend MORE than $400, but you can always spend LESS, the constraint inequality is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 55x\ +\ 13y\ \leq\ 400]


An equation of the boundary line of the constraint inequality is found by replacing the inequality sign with an equals sign.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 55x\ +\ 13y\ =\ 400]


Then add *[tex \LARGE -55x] to both sides and multiply both sides by *[tex \LARGE \frac{1}{13}] to put the equation into slope-intercept form.


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