Barbour Corporation, located in Buffalo, New York, is a retailer of high$-$tech products and is known for its excellent quality and innovation. Recently, the firm conducted a relevant cost analysis of one of its product lines that has only two products, T$-1$ and T$-2.$ The sales for T$-2$ are decreasing and the purchase costs are increasing. The firm might drop T$-2$ and sell only T$-1.$

Barbour allocates fixed costs to products on the basis of sales revenue. When the president of Barbour saw the income statements $($see below$),$ he agreed that T$-2$ should be dropped. If T$-2$ is dropped, sales of T$-1$ are expected to increase by $10$ percent next year, but the firm$$s cost structure will remain the same.

T$-1$ T$-2$

Sales $ $225,000$ $ $280,000$

Variable costs:

Cost of goods sold $75,000140,000$

Selling & administrative $37,50055,000$

Contribution margin $ $112,500$ $ $85,000$

Fixed expenses:

Fixed corporate costs $65,00080,000$

Fixed selling and administrative $17,00026,000$

Total fixed expenses $ $82,000$ $ $106,000$

Operating income $ $30,500$ $ $(21,000)$

Required:

$1.$ Find the expected change in annual operating income by dropping T$-2$ and selling only T$-1.$

$2.$ By what percentage would sales from T$-1$ have to increase in order to make up the financial loss from dropping T$-2?($Enter your answer as a percentage rounded to $2$ decimal places $($i$.$e$.0\mathrm{.}1234$ should be entered as $12\mathrm{.}34).)$

$3.$ What is the required percentage increase in sales from T$-1$ to compensate for lost margin from T$-2,$ if total fixed costs can be reduced by $$47,000?($Enter your answer as a percentage rounded to $2$ decimal places $($i$.$e$.0\mathrm{.}1234$ should be entered as $12\mathrm{.}34).)$