The running costs of a particular factory consist of two components – a constant charge per week for rent of premises and a variable cost for labour which depends on the number of staff working in the factory in that particular week.
The total weekly running costs are $20 000 when there are 25 staff and $35 000 when there are 50 staff working the factory.
Write an equation that describes the relationship between the total cost, C, and the number of staff, n.
Use your equation to calculate the total weekly cost when 35 staff are working the factory.
Look at it as being given 2 ordered pairs
(25,20000) and (50,30000), and being asked to find the equation of the straight line.
Your general point will be (n,C)
slope = (30000-20000)/(50-25) = 400
now you have the slope and using one of the given points, find the equation using the method that was taught to you.
For the last part, sub in n = 35, then find C
To find the equation that describes the relationship between the total cost (C) and the number of staff (n), we can use the information given.
We know that the running costs of the factory consist of a constant charge for rent and a variable cost for labor.
Let's denote the constant charge for rent as A and the variable cost for labor per staff as B.
According to the information given, when there are 25 staff, the total weekly cost is $20,000, and when there are 50 staff, the total weekly cost is $35,000.
Using this information, we can set up two equations:
When n = 25:
C = A + B * n
20000 = A + B * 25
When n = 50:
C = A + B * n
35000 = A + B * 50
Now, we have a system of two equations that we can solve to find the values of A and B.
By subtracting the first equation from the second equation, we can eliminate A:
35000 - 20000 = A + B * 50 - (A + B * 25)
15000 = B * 50 - B * 25
15000 = 25B
B = 15000/25
B = 600
Now, we can substitute the value of B into any of the original equations to find the value of A. Let's use the first equation:
20000 = A + 600 * 25
20000 = A + 15000
A = 20000 - 15000
A = 5000
Therefore, the equation that describes the relationship between the total cost (C) and the number of staff (n) is:
C = 5000 + 600n
To find the total weekly cost when 35 staff are working at the factory, we substitute n = 35 into the equation:
C = 5000 + 600 * 35
C = 5000 + 21000
C = 26000
So, the total weekly cost when 35 staff are working at the factory is $26,000.