00:01
In this question we have a farmer who is growing potatoes and corn.
00:06
So for this some conditions are given in the equation.
00:11
First of all let the area in acres used for planting potatoes let this is represented by x and for corn area is represented by y.
00:25
So clearly since x and y are areas so these will be always greater than or equal to 0.
00:32
Also we are given that total area which can be used for planting is 70 acres.
00:39
So that means x plus y will be less than or equal to 70.
00:45
Let this be equation number 1.
00:47
Now we are given that cost for planting potatoes in 1 acre is equal to $20.
01:04
So cost of planting potatoes in x acres will be equal to 20x.
01:17
Similarly cost of planting corn in 1 acre is $60.
01:26
So cost of planting corn in y acres will be equal to 60y.
01:35
Also total cost that he can use for planting is 3000.
01:40
So that means 20x plus 60y will be less than or equal to 3000 because this is the maximum cost which he can use.
01:50
But if we take 20 common and take it to the right hand side.
01:54
So 3000 divided by 20 will be equal to 150.
01:59
So let this be equation number 2.
02:01
Now third condition is given on profit.
02:05
Profit on potatoes is equal to $150 per acre.
02:17
And profit on corn is equal to $50 per acre.
02:28
So for x acres profit will be 150x and for y acres profit will be 50y.
02:34
That means the profit function will be equal to 150x plus 50y.
02:42
So we have to find out the value of x and y so that we can maximize the profit.
02:48
So basically this is the profit function from equation 1 and 2.
02:52
We have x plus y less than equal to 70 and x plus 3y is less than equal to 150.
03:01
Where x and y both are greater than equal to 0.
03:04
So we can solve this graphically for this.
03:09
We will have two points if we have to plot it on the graph.
03:13
So we need at least two points.
03:15
So when x is 0, y is 70, y is 0, x is 70.
03:19
For this two points will be.
03:24
So when x is 0, y is 50 and when y is 0, x is 150.
03:30
Now plotting these two points on the graph.
03:36
So this is the coordinate plane.
03:41
Here we have 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150.
04:07
Similarly here we will have 10, 20, 30, 40, 50, 60, 70, 80, 90 and so on.
04:22
So when x is 0, y is when y is 0, x is 70, x is 0, y is 70.
04:28
So joining these two points.
04:33
This will be the plot for x plus y equal to 70...