A centre enters students for English levels one and two end test every year. Some take the paper based version, others online version.
For planning purposes you need to assume trend patterns indicate that
.the total number of entries each year is always more than 50
.the number of level one entries never exceeds four times the number number of level two entries
.80% of level one entries are registerd for the online version compared with only 20% of level two entries.
The max yrly budget for all entries is £400. The cost of entering students for online versions is £5 and paperbased entries cost £10
By setting up a series of linear ineqalities and representng these graphically, find the maximum number of level two entries in any one year.
.Please use the info given to set up three linear inequalities
.plot these on graph paper and identify the area in which the solution lies
.use the graph to find the maximum number of level two entries for any one year.
To find the maximum number of level two entries in any one year, we can set up three linear inequalities based on the given information. Let's define the variables as follows:
L1 = Number of level one entries
L2 = Number of level two entries
1. The total number of entries each year is always more than 50:
L1 + L2 > 50
2. The number of level one entries never exceeds four times the number of level two entries:
L1 <= 4L2
3. 80% of level one entries are registered for the online version, compared with only 20% of level two entries:
0.8L1 * £5 + 0.2L2 * £10 <= £400
Now, let's plot these inequalities on a graph:
On the horizontal axis, let's represent the number of level one entries (L1), and on the vertical axis, let's represent the number of level two entries (L2).
1. Plot the line L1 + L2 = 50:
Plot the points (0, 50) and (50, 0) and draw a line passing through these points.
2. Plot the line L1 = 4L2:
Plot the points (0, 0), (1, 4), and (4, 16) and draw a line passing through these points.
3. Plot the line 0.8L1 * £5 + 0.2L2 * £10 = £400:
Rearrange the equation to get 0.4L1 + L2 = 4:
Plot the points (0, 4), (10, 0), and (40, 0) and draw a line passing through these points.
Now, the area where all three inequalities intersect represents the feasible region. Find the corner point within this region that maximizes L2, which will give us the maximum number of level two entries in any one year.
By analyzing the graph, you can determine the maximum number of level two entries for any one year.