What should be the price charged to the customer for repairs to the dishwasher? (All calculations to nearest pence.)

Steps to Solve

1. Calculate Total Direct Costs
   First, we need to sum the direct materials and direct labor to get the total direct costs.
   The direct materials cost is £88 (for parts), and the direct labor cost is for 4 hours of technician work.
   The hourly rate for direct labor can be calculated as:

$$ \text{Direct Labor Cost} = \frac{\text{Total Direct Labor}}{\text{Total Direct Labor Hours}} \times \text{Hours Worked} $$

Using the total direct labor of £31,000 for an unspecified number of hours (assumed to be 2100), we can find the hourly rate:

$$ \text{Hourly Rate} = \frac{31,000}{2,100} = £14.76 $$

So, for 4 hours, the direct labor cost is:

$$ \text{Direct Labor Cost} = 4 \times 14.76 = £59.04 $$

Now, add the direct materials and direct labor costs:

$$ \text{Total Direct Costs} = 88 + 59.04 = 147.04 $$

2. Calculate Overhead Costs
   Next, overhead is applied based on the direct labor costs and calculated as an additional 40%.
   To calculate overhead:

$$ \text{Overhead} = \text{Direct Labor Cost} \times 0.40 = 59.04 \times 0.40 = 23.616 $$

3. Calculate Total Cost
   Now sum the total direct costs and the overhead costs to get the total cost before profit markup:

$$ \text{Total Cost} = \text{Total Direct Costs} + \text{Overhead} = 147.04 + 23.616 = 170.656 $$

4. Apply Profit Markup
   Finally, apply the profit markup to the total cost. The profit markup here is an additional £40 (as stated in the problem).

$$ \text{Final Price} = \text{Total Cost} + 40 = 170.656 + 40 = 210.656 $$

5. Round to Nearest Pence
   Since the price needs to be rounded to the nearest penny, the final charge to the customer is:

$$ \text{Final Charge} = £210.66 $$