Question 981186
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Your objective function is correct, but your constraint inequalities are completely off-base.


Neither worker will work more than 42 hours per week.  The number of hours that Tom spends making x tables is 2x and the number of hours that he spends making y tables is 3y, so the total time he spends working in a week is 2x + 3y hours.  This amount must be less than or equal to 42.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x\ +\ 3y\ \leq\ 42]


Likewise, for the other guy


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6x\ +\ 2y\ \leq\ 42]


Then you must include the non-negative constraints and you should also constrain your variables to the integers since you wouldn't be able to sell a fractional part of a chair or a table.


Once you graph these correct constraint inequalities you will locate your correct answer.  Here's a hint for graphing these problems: Always shade the inequalities with the OPPOSITE sense.  That way, the feasible area, rather than being a rather difficult to discern "most dense shading" area, is the easily seen completely un-shaded area.  Just make sure to annotate your graphs when you do this so that you don't confuse your instructor.


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

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \