<PRE><B>Question 271218</B>
A radio manufacturing company makes two styles of radio – battery powered and solar powered.
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The battery powered radio requires 2 hours of testing and 3 hours of assembly,  the solar powered radio requires 4 hours of testing and 2 hours of assembly. 
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If 56 hours are available for testing and 72 hours are available for assembly, how many of the two types of radio should be made to maximize profit? 
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Testing Inequality: 2x + 4y &lt;= 56
Assembly Inequality 3x + 2y &lt;= 72
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The profit for the battery powered radio is $35 while the profit for the solar powered radio is $40.
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Objective Function: Profit = 35x + 50y
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Graph the Testing and the Assembly Inequality in the 1st quadrant
because x&gt;=0 and y&gt;=0
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{{{400.300,-10,10,-10,10,(-1/2)x+14,(-3/2)x+36)}}}
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Find the point of intersection of the two boundary lines:
(-1/2)x+14 = (-3/2)x+36
x = 12
y = 8
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Find the vertices of the inclosed n-gon:
(0,14),(8,12),(0,0),(28,0
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Test the Profit associated with each of these in the Objective equation
to find which pair has the maximum Profit.
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Profit = 35x + 50y
(0,14) yields 50*14 = 700
(8/12) yields 8*35+12*50 = 880
(0,0) yields 0
(28,0) = 28*35 = 980
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Maximum comes from manufacturing 28 battery powered and no solar.
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Note: You should check my arithmetic.  The method is correct but
I may have missed something on the adding etc.
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Cheers,
Stan H.
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I know that x will represent the battery powered radio and y will represent the solar powered radio. I&#39;m not sure how to set this problem up though. I know it will involve inequalities. How do I find the minimum and maximum values? What is the difference between the constraint and the objective? Which one represents the equation? Do I graph it like a normal inequality? I think the vertices is the point where they intersect. Is this right?</PRE>