Question

4. philip wants to use television advertising to maximize his brand exposure so he negotiates an expense reduction to $75,000. how many shirts would he have to sell to achieve a 40 percent profit margin with the reduced expense?

Answer 1

To achieve a 40 percent profit margin with the reduced expense, Philip would have to sell approximately 1.4 shirts.

Step-by-step explanation:

To calculate the number of shirts Philip would have to sell to achieve a 40 percent profit margin with the reduced expense, we need to consider the cost of each shirt and the desired profit margin.

Let's assume the cost of each shirt is $x. The reduced expense, after negotiation, is $75,000. The profit margin is 40 percent, which means that Philip wants to make a profit of 40% of the cost price.

So, the equation to calculate the number of shirts can be written as:

Revenue - Cost = Profit

Let's calculate:

Revenue = Number of shirts sold * Sale price

Cost = Number of shirts sold * Cost per shirt

Profit = Revenue - Cost

Given Revenue = Cost + Profit

Revenue = $75,000 + 40% of Cost

Now, to maximize the brand exposure, let's assume that Philip wants to sell all the shirts. Therefore, the revenue will equal the reduced expense.

This gives us:

$75,000 = $x * (1 + 0.40)

Simplifying the equation:

$75,000 = $x * 1.40

Divide both sides of the equation by 1.4:

$x = $75,000 / 1.4

Solve for x:

$x ≈ $53,571.43

So, the cost of each shirt is approximately $53,571.43.

Now, let's calculate the number of shirts needed to achieve a 40 percent profit margin with the reduced expense:

$75,000 = Number of shirts * $53,571.43

Solve for the number of shirts:

Number of shirts ≈ $75,000 / $53,571.43

Number of shirts ≈ 1.4

Therefore, Philip would have to sell approximately 1.4 shirts to achieve a 40 percent profit margin with the reduced expense.