Question

"Concorde Ltd has been asked to quote a price for an order of 8 units of Product Delta. Making this product will require skilled​ labour, which is currently in short supply and is paid £15 an hour. If the order is​ accepted, all necessary labour will have to be transferred from existing work. As a​ result, other orders will be lost. It is estimated that for each hour transferred to this contract £50 will be lost​ (calculated as lost sales revenue £​80, less materials £15 and labour £​15). The production manager believes​ that, owing to a learning​ process, the time taken to make each unit will​ reduce, from 20 hours to make the first​ one, by one hour a unit made.​ (That is 20 hours to make the first​ one, 19 hours to make the​ second, 18 hours to make the third one and so​ on.)"

What is the total relevant cost of skilled labour for the purposes of the​ order?
a) £420
b) £480
c) £540
d) £600

Answer 1

The total relevant cost of skilled labor for the order of 8 units of Product Delta is £540.

Step-by-step explanation:

The total relevant cost of skilled labour for the order can be calculated by multiplying the number of units of Product Delta by the time taken to make each unit and the cost of skilled labor per hour. According to the information provided, the time taken to make each unit decreases by one hour for each unit made. So, the total time taken to make 8 units can be calculated as follows:

1. The time taken to make the first unit = 20 hours
2. The time taken to make the second unit = 19 hours
3. The time taken to make the third unit = 18 hours
4. And so on...

The total relevant cost of skilled labor for the order can be calculated by summing up the cost of labor for each unit:

• For the first unit: £15 x 20 hours = £300
• For the second unit: £15 x 19 hours = £285
• For the third unit: £15 x 18 hours = £270
• And so on...

To find the total relevant cost of skilled labor:

Total cost = £300 + £285 + £270 + ...

This is an arithmetic series with a common difference of -1 and the first term of 300. Using the formula for the sum of an arithmetic series, the total relevant cost of skilled labor can be calculated as:

Total cost = (n/2)(2a + (n-1)d) = (8/2)(2(300) + (8-1)(-15)) = £540

Therefore, the total relevant cost of skilled labor for the order is £540.