Sec$-$Tech Co$.$ is a software corporation that is evaluating the production of a new hardware product for WID $($wireless Intrusion Detection$)$ and governmental agencies are their main customers. The capital cost of the new production plant is expected to be $$7,500,000$ with annual maintenance costs of $3\%$ of capital. Other annual fixed costs include $$185,000$ for utilities, administrative salaries are $$135,000$ per year and insurance is expected to be $$78,000.$ The plant will depreciate over $20$ years with a salvage value of $$950,000($use straight line method$).$ Other fixed costs are estimated to be $$165,000$ per year. Variable costs can be broken down into materials: SmartEdge sensor at $$600$ per device; a Power Injector at $$270$ per device and other materials at $$978$ per device; and direct labor at $$23\mathrm{.}5$ per labor hour with fringe benefits estimated at $22\%$ of the direct labor cost. Sec$-$Tech has run several forecast scenarios for different selling prices $($based on the potential agencies that will become their customers$)$ and the results are presented in the table below:

Average Sales Price $($$$/$device$)-$ Sales $($in units$)$

$$1,725\mathrm{.}00-10,000$

$$1,900\mathrm{.}00-9,000$

$$2,005\mathrm{.}00-7,500$

$$2,105\mathrm{.}00-6,250$

$$2,300\mathrm{.}00-5,500$

$$2,700\mathrm{.}00-4,750$

$$2,825\mathrm{.}00-3,875$

Develop a breakeven capacity analysis for Sec$-$Tech$$s new device and determine:

a$.$ Best price, production rate, and profit.

b$.$ Breakeven production rate with the price determined in part a$.$

c$.$ Breakeven price with the production rate determine in part a$.$

d$.$ Sensitivity of profits to: i$)$ a $25\%$ increase $($and decrease$)$ in variable costs; ii$)$ a $17\%$ increase $($and decrease$)$ in the selling price; iii$)$ an $8\%$ increase $($and decrease$)$ in the production rate.