Let's solve this step-by-step.
### Part (a):
To determine the markup and selling price, follow these steps:
#### Step 1: Calculate the operating expenses per unit.
Given that the operating expenses are 20% of the unit cost:
[tex]\[
\text{Operating expenses per unit} = 0.20 \times 800 = 160
\][/tex]
#### Step 2: Calculate the desired operating profit per unit.
Given that the desired operating profit per unit is 15% of the unit cost:
[tex]\[
\text{Desired operating profit per unit} = 0.15 \times 800 = 120
\][/tex]
#### Step 3: Calculate the total markup.
The markup is the sum of the operating expenses per unit and the desired operating profit per unit:
[tex]\[
\text{Markup} = 160 + 120 = 280
\][/tex]
#### Step 4: Calculate the selling price.
The selling price is the sum of the unit cost and the markup:
[tex]\[
\text{Selling price} = 800 + 280 = 1080
\][/tex]
So, the markup is [tex]$280 and the selling price is $[/tex]1080.
### Part (b):
To find the rates of markup on cost and on selling price, follow these steps:
#### Step 1: Calculate the rate of markup on cost.
The rate of markup on cost is given by the percentage of markup relative to the unit cost:
[tex]\[
\text{Rate of markup on cost} = \left(\frac{\text{Markup}}{\text{Unit cost}}\right) \times 100 = \left(\frac{280}{800}\right) \times 100 = 35\%
\][/tex]
#### Step 2: Calculate the rate of markup on selling price.
The rate of markup on selling price is given by the percentage of markup relative to the selling price:
[tex]\[
\text{Rate of markup on selling price} = \left(\frac{\text{Markup}}{\text{Selling price}}\right) \times 100 = \left(\frac{280}{1080}\right) \times 100 \approx 25.93\%
\][/tex]
So, the rate of markup on cost is 35% and the rate of markup on selling price is approximately 25.93%.
