Solve the following linear program using the graphical solution procedure: Max 5A + 5B s.t. 1A lessthanorequalto 100 1B lessthan
orequalto 80 2A + 4B lessthanorequalto 400 A, B greaterthanorequalto 0
1 answer:
<h2>Answer:</h2>
- The optimal solution to the given linear programming problem exist at (100,50)
- and the optimal solution is: 5A+5B= 750
We are given a system of linear programming problem as follows:
Max 5A + 5B
s.t. A ≤ 100---------------(1)
B ≤ 80-------------(2)
2A+4B ≤400-------------(3)
which is given by:
A+2B ≤ 200
and A,B≥0
This means that the solution to this LPP will lie in the first quadrant.
( Since, both the variables A and B are greater than or equal to zero)
Now, we consider that A is represented by the x axis and B by y-axis.
We know that the optimal solution always exist at the boundary point.
Hence, by plotting these inequalities in the graph we get the boundary points as:
(0,0) , (0,80) , (100,0) , (100,50) and (40,80)
Now, we will check at which boundary point the optimal function is maximized .
Point Value of optimal function( 5A+5B)
(0,0) 0
(0,80) 400
(100,0) 500
(100,50) 750
(40,80) 600
The maximum value is obtained at (100,50).
and the value of the optimal solution is: 750
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Answer:
c = 5√5
Step-by-step explanation:
When we have a right triangle, there is a property about its measurements that is <em>always</em> true, and its called the "Pythagorean Theorem"
First, let's understand the basic terms we use to describe the sides of a triangle:
we can call one leg "a", the other leg "b" and the slanted side "c"
("c" is also called the hypotenuse--and it's always opposite the 90-degree angle)
the pythagorean theorem:
a² + b² = c²
here, our "a" is 5, our "b" is 10 {and we don't know what c is}
let's try plugging these values into our formula:
a² + b² = c²
5² + 10² = c²
25 + 100 = c²
125 = c²
now, we know what c² is--but we want to know c,
so we must take the square root of both sides
√125 = √c²
√125 = c
now, while √125 <em>is </em>our answer, we can simplify further!
this is because 125 can be made up of 5 · 25
so,
and
we can take out the square root of 25 (5):
we write this as such:
so, in simplest radical form, c = 5√5
(√125)
hope this helps!! have a lovely day :)