Which expression is best for finding the area of the polygon?
1 answer:
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The region in the graph that represents the solution of the system of linear inequalities y ≥ 2x − 3 and y ≤ -x + 1 is given by C region , This can be clearly understood from the graph attached.
<h3>What is Inequality ?</h3>When two algebraic expressions are equated by an inequality operator then the mathematical statement formed is called inequality
It is given that a line passes through the points (0, 1) and (2, minus 1)
The equation of the line representing this is given by
y = mx+c
m = -1
y = -x+1
and the other line passing through the points of (0, minus 3) and (2, 1) is
m = 2
y = 2x -3
These are plotted on the graph
From intersection, region to the right of it is A, below is D, to the left is C, and above is B.
These are noted ion the graph
Then the inequalities are plotted y ≥ 2x − 3 and y ≤ -x + 1
The region in the graph that represents the solution of the system of linear inequalities y ≥ 2x − 3 and y ≤ -x + 1 is given by C region , This can be clearly understood from the graph.
To know more about Inequality
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Answer:
Optimal production = 600 gold pens
Revenue = 600*7 = $4200 gold pens
Step-by-step explanation:
The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model.
A. The silver model requires 1 minute in a grinder and 3 minutes in a bonder.
B. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder.
Because of maintenance procedures,
C. the grinder can be operated no more than 30 hours per week and
D. the bonder no more than 50 hours per week.
The company makes
E. $5 on each silver pen and
F. $7 on each gold pen.
How many of each type of pen should be produced and sold each week to maximize profits?
Solution:
We will solve the problem graphically, with number of silver pens, x, on the x axis, and number of gold pens, y, on the y axis, i.e.
1. From A and C, the maximum number of silver pens
x <= 30*60 / 1 = 1800 and
x <= 50*60 /3 = 1000 ....................(1) bonder governs
2. from A & D, the maximum number of gold pens
y <= 30*60 / 3 = 600 .....................(2) grinder governs
y <= 50*60 / 4 = 750
3. From D,
x + 3y <= 30*60 = 1800 ...................(limit of grinder) ..... (3)
3x + 4y <= 50*60 = 3000 .................(limit of bonder) .......(4)
Need to maximize profit,
Z(x,y) = 5x+7y, represented by parallel lines y = -5x/7 + k such that all constraints of (3) and (4) are satisfied.
The maximum is obtained when Z passes through (360,480), i.e. at intersection of constraints (3) and (4). Using slope intercept form,
(y-480) = -(5/7)(x-360)
or y=-(5/7)x + (737+1/7) [the purple line] which violates the red line, so not a solution.
Next try the point (0,600)
(y-600) = -(5/7)(x-0), or
y = 600 - (5/7)x [the black line]
As we can see all point on the black (in the first quadrant) satisfy the constraints, so it is a feasible solution, and is the optimal solution, with a revenue of
Revenue = 600*7 = 4200 gold pens
