Question 23072: Hi, I need to do problem on linear programming and answer all those questions bellow the problem. This is a problem: A manufacturer produces two kinds of radios.
Model X takes 4 hours to produce, cost $8 in production, and sells for $15
Model Y takes 3 hours to produce, cost $7 in production, and sells for $12
If manufacture allots a total of 58 hours and $126 per week to produce radios, find his maximum income. How many of each model will produce this maximum profit?
X stands for: I think x stand for number model X radios will produces
Y stands for: I think y number model Y radios will produces
Constraint Equations:
8x+ 7y
15x+12y
I think if I know how to create equation then I will be able to to graphs
Objective Function:
Corner Coordinates:
Work shown in checking Coordinates:
Correct answer in a sentence
Graph
Answer by stanbon!(97)   (Show Source):
You can put this solution on YOUR website! Regarding your constraint equations:
8x+7y is a production cost expression. The equation
you want is 8x+7y<=126
You also need a production time eqation:
4x + 3y <= 58
Also x>=0 and y>=0
The Objective Function is an Income statement:
Income or I = 15x + 12y
Procedure:
Graph the four constraint lines on a single pair of xy axes.
The lines will form a triangle with two intersections on the
y-axis and one where the production-cost and the production-
time lines intersect.
Find the three points of intersection.
Put the (x,y) values into the objective function to determine
under what production conditions you maximize your income and
therefore your maximize profit.
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