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.
Cost = fixed cost + variable cost*# staff
C = f + k*x
20000 = f + 25k
35000 = f + 50k
subtract to get
25k = 15000
k = 600
so, C(x) = 5000 + 600x
and C(35) = 5000 + 600*35 = 26000