$[$The following information applies to the questions displayed below.$]$

Lightening Bulk Company is a moving company specializing in transporting large items worldwide. The firm has an $85\%$ on$-$time delivery rate. Thirteen percent of the items are misplaced and the remaining $2\%$ are lost in shipping. On average, the firm incurs an additional $$68$ per item to track down and deliver misplaced items. Lost items cost the firm about $$345$ per item. Last year, the firm shipped $6,810$ items with an average freight bill of $$227$ per item shipped.

The firm$$s manager is considering investing in a new scheduling and tracking system costing $$155,000$ per year. The new system is expected to reduce misplaced items to $1\%$ and lost items to $0\mathrm{.}50\%.$ Furthermore, the firm expects total sales to increase by $10\%$ with the improved service. The average contribution margin ratio on any increased sales volume, after cost savings associated with a reduction in misplaced and lost items, is expected to be $37\mathrm{.}5\%.$

Required:

$1$a$.$ Based on a relevant cost analysis, should the firm install the new tracking system?

multiple choice

Yes

No

$1$b$.$ What is the estimated change in pretax cash flow under the proposed system? $($Negative amounts should be indicated by a minus sign. Round your answers to the nearest whole dollar amount.$)$

$3.$ Upon further investigation, the manager discovered that $80\%$ of the misplaced or lost items either originated in or were delivered to the same country. What is the maximum amount the firm should spend to reduce the cost of problems in that country by $90\%?($Round your intermediate calculations and final answer to the nearest whole dollar amount.$)$