Question 166542: can someone please show me how to do this problem:
Find the value(s) of the function, subject to the system of inequalities.
Find the minimum of P = 23x + 21y + 22 subject to:
x (greater than or equal to) 0, y ( greater than or equal to) 0, x + y (greater than or equal to) 1.
a. 66
b. 43
c. 45
d. 22
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! your constraints are:
x >= 0
y >= 0
x+y >=1
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since the equation is 23*x and 21*y, you want to make x = 0 which will be the smallest term you can use for x or y.
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if you make x = 0, then x + y >=1 becomes y >= 1 which means you want to make y = 1 because 1 is the smallest it can become.
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assuming x = 0 and y = 1, the results of the equation become:
23*0 + 21*1 + 22 = 43.
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the smallest value of your equation is 43 which is option b.
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if you had made y = 0, then x would have had to have been 1, and your equation would have become:
23*1 + 21*0 + 22 = 45
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option b is your answer and the values you had to use are:
x = 0
y = 1
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