Price reductions are often an effective way to increase sales, but marketers need to analyze how much sales must increase before a price reduction pays off. Consider a small chain of retall dothing stores with $10$ locations in the eastern U$.$S$.$ that specializes in upscale, trendy clothing for teens and young adults. Just $10$ years ago, fotal revenues for the chain were nearly $$7$ million. In the face of a weak economy and an intensively competitive retail environment, total revenues have declined significantly, falling to $$6$ million in $20x.$

The owners of the chain are considering an across$-$the$-$board price reduction to increase revenue. Assuming that the chain's gross margin is $65\%$ and that cost of goods sold is the only variable cost, how much do sales need to increase to maintain the same gross profit in absolute dollars if the chain cuts prices by $5\%?$

The current gross profit is $$3\mathrm{.}90$ million. $($Round to two decimal places.$)$

Set the initial price equal to $$1\mathrm{.}00.$ Then the new price is $$0\mathrm{.}95.($Round to the nearest cent.$)$

The new gross margin percentage in decimal form equals $($Round to four decimal places.$)$