Miles Audio produces and sells car audio systems. They specialize in receivers and currently offer two models. The Growler is a high quality but affordable unit that the company produces for sale in auto parts and electronics stores. The Maniac is sold almost solely to individuals and high$-$end car stereo installers. The Maniac is only produced to order. In other words, the Maniac is not kept in inventory and is only produced when a customer orders one. Based on estimates of next quarter's business, the financial staff at Miles has produces the following forecasted income statement.

Growler Maniac Total

Number of systems $2,4004502,850$

Sales revenue $ $480,000$ $ $405,000$ $ $885,000$

Materials $ $91,200$ $ $69,750$ $ $160,950$

Labor $108,000101,250209,250$

Materials inspection $54,72041,85096,570$

Factory lease $33,15017,85051,000$

Utilities $14,6907,91022,600$

Miscellaneous factory costs $27,30014,70042,000$

Sales and administration $142,130$

Total costs $ $724,500$

Operating profit $ $160,500$

Firm orders have already been placed with Miles for the $450$ Maniac systems reflected in the forecasted quarterly income statement. Materials inspection varies with material cost. The labor wage rate at Miles $($excluding variable overhead$)$ is $$30$ per hour. The factory lease, utilities, and miscellaneous factory costs are allocated to the product lines based on the amount of floor space occupied. Sales and administration costs are not allocated to the two product lines.

Lanoo Custom Systems, a custom car audio shop, has called Miles and asked about placing an order for the upcoming quarter for $100$ units of the Maniac. Miles Audio is already scheduled to work at capacity in the next quarter and would have to give up some other business to fulfill this order. Miles is committed to the orders for the Maniac it already has accepted but can reduce the number of Growler systems produced in the next quarter to $1,900.$ Miles would not be able to make up the losses from the reduced Growler sales as the market is quite competitive and customers for this relatively standard system will buy another product. Miles also is expecting to be operating at close to full capacity for the foreseeable future, which is another reason the lost Growler systems could not be replaced later. The customer is willing to pay a premium price of $$940$ for the special order. The factory lease, utilities, miscellaneous factory costs, and sales and administration would not be affected by the special order.

Required:

a$-1.$ Calculate the differential operating profit $($loss$).$

a$-2.$ From an operating profit $($loss$)$ perspective for March, should Miles Audio accept the order from Lanoo Custom Systems?

b$.$ What is the minimum price Miles Audio should accept to take the special order from Lanoo Custom Systems?