Which phrases can be used to represent the inequality 12 minus 3 x greater-than-or-equal-to 9? Select two options.
2 answers:
Check attachment for the remaining part of the questions.
Answer:
The correct options are:
C. Twelve less three times a number is at least nine.
F. Twelve minus the product of three and a number is no smaller that nine.
Step-by-step explanation:
Given 12 - 3x ≥ 9,
we want to check which phrase from the options can be used to represent the inequality.
12 - 3x: This means the product of 3 and a number is subtracted from 12.
≥: This is the "Greater or equal to" symbol. It is used to show that the quantity on the left hand side of the symbol is at least, the exact quantity on the right. It means the quantity on the right hand side can be equal, or greater, but can never be smaller the quantity on the left hand side.
So, the statement means
When 3 is multiplied my a number, and then the result is subtracted from 12, what we have is at least 9.
The only statements that corresponds to this from the options are:
1. Twelve less three times a number is at least nine.
2. Twelve minus the product of three and a number is no smaller that nine.
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Answer:
Hence, (75,40) is the maximum point and maximum profit is $192.5
Step-by-step explanation:
Let the breakfast be x
And let the lunch or afternoon be y
Inequalities will become
And objective function will be
Z=1.5x+2.0y
You can see the graph in the attachement
ABCD is the feasible region
Points of feasible region is (0,90) ,(0,0) ,(75,40) and(105,0)
We have to find Z by substituting the points of feasible region
At (0,90) we get
Z=1.5(0)+2(90)
Z=180
At (0,0)
Z=1.5(0)+2(0)
Z=0
At (75,40)
Z=1.5(75)+2(40)
Z=192.5
At (105,0)
Z=1.5(105)+2(0)
Z=157.5
The maximum number we are getting is 192.5 which is at (75,40)
Hence, (75,40) is the point of maximum
