Question 1166693
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A chain saw requires 3 hours of assembly and a wood chipper 7 hours. A maximum of 42 hours of assembly time is available. 
The profit is $190 on a chain saw and $210 on a chipper. 
How many of each should be assembled for maximum​ profit?
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<pre>
Let x be the number of wood chippers.

Then the number of chain saws is  {{{(42-7x)/3}}}.


The profit function is  P = {{{210x + 190*(42-7x)/3}}}.     (*)


Next, in order for do not spend my time for nothing, I create a Table in Excel with 3 column.


First column is   x = 0, 1, 2, 3,4, 5, 6, 7.


Second column is  {{{(42-7x)/3}}} to see when this number is integer.


The third column is the profit by formula (*).


       T       A       B       L       E

 
   x           {{{(42-7x)/3}}}          Profit P = {{{210x + 190*(42-7x)/3}}}

--------------------------------------------------------------


   0            14                      2660
   1		11.66666667		2426.666667
   2		9.333333333		2193.333333
   3		7			1960
   4		4.666666667		1726.666667
   5		2.333333333		1493.333333
   6		0			1260
   7		-2.333333333		1026.666667
</pre>

From the &nbsp;Table, &nbsp;you see the &nbsp;<U>ANSWER</U> :  &nbsp;&nbsp;0 wood chippers &nbsp;and &nbsp;14 chain saws.


Solved.