George’s Break-Even Price Calculation
To determine George’s break-even price per shirt, we can use the formula:
[ \text{Break-even price per shirt} = \frac{\text{Total Fixed Costs}}{\text{Total Number of Shirts Produced}} + \text{Marginal Cost per Shirt} ]
Given:
– Total Fixed Costs = $30,000
– Number of Shirts Produced = 10,000
Substitute the values into the formula:
[ \text{Break-even price per shirt} = \frac{30,000}{10,000} + 2 = 3 + 2 = 5 ]
Therefore, George’s break-even price per shirt is $5.
Impact of Selling 50% More T-Shirts
If George sells 50% more T-shirts per month, the new quantity of shirts produced will be:
[ \text{New Quantity of Shirts Produced} = 10,000 + (0.5 \times 10,000) = 10,000 + 5,000 = 15,000 ]
Now, we can calculate the new break-even price per shirt using the updated quantity:
[ \text{New Break-even price per shirt} = \frac{30,000}{15,000} + 2 = 2 + 2 = 4 ]
Therefore, if George sells 50% more T-shirts per month, his break-even price per shirt decreases to $4.
In conclusion, by increasing the number of T-shirts sold, George can lower his break-even price per shirt, making his business more competitive in the market.
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