SOLUTION: 2. A radio manufacturing company makes two styles of radio � battery powered and solar powered. The battery powered radio requires 2 hours of testing and 3 hours of assembly, while

Question 271218: 2. A radio manufacturing company makes two styles of radio � battery powered and solar powered. The battery powered radio requires 2 hours of testing and 3 hours of assembly, while the solar powered radio requires 4 hours of testing and 2 hours of assembly. 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? The profit for the battery powered radio is $35 while the profit for the solar powered radio is $40.
I know that x will represent the battery powered radio and y will represent the solar powered radio. I'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? Please help!
Thank you!
Shawn
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A radio manufacturing company makes two styles of radio � battery powered and solar powered.
-----------------------------
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.
-----------------------------
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?
-----------------------------------------------------------------
Testing Inequality: 2x + 4y <= 56
Assembly Inequality 3x + 2y <= 72
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The profit for the battery powered radio is $35 while the profit for the solar powered radio is $40.
----
Objective Function: Profit = 35x + 50y
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Graph the Testing and the Assembly Inequality in the 1st quadrant
because x>=0 and y>=0
---

----------
Find the point of intersection of the two boundary lines:
(-1/2)x+14 = (-3/2)x+36
x = 12
y = 8
-------
Find the vertices of the inclosed n-gon:
(0,14),(8,12),(0,0),(28,0
------
Test the Profit associated with each of these in the Objective equation
to find which pair has the maximum Profit.
------------------------------------
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.
===============================================
Cheers,
Stan H.
===============================================

I know that x will represent the battery powered radio and y will represent the solar powered radio. I'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?
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