Troy Engines, Ltd$.,$ manufactures a variety of engines for use in heavy equipment. The company usually produces all of the necessary parts for its engines, including all of the carburetors. An outside supplier has offered to produce and sell one type of carburetor to Troy Engines, Ltd$.,$ for a cost of $$35$ per carburetor. To evaluate this offer, Troy Engines, Ltd$.,$ has gathered the following information relating to its own cost of producing this carburetor internally:

Per $15,000$ Carburetors

Carburetor per Year

Direct materials $($variable$)$ $$14$ $$210,000$

Direct labor $($variable$)10150,000$

Variable manufacturing overhead $345,000$

Fixed manufacturing overhead $($FMOH$),$ traceable $6*90,000$

Fixed manufacturing overhead $($FMOH$),$ allocated $9**135,000$

Fixed selling costs, allocated $230,000$

Total cost $$44$ $$660,000$

$*$ One$-$third of the traceable FMOH is supervisory salaries, a step cost. One supervisor is required for every $15,000$ carburetors. The one supervisor now employed can be laid off if product is outsourced. The remainder of the traceable FMOH represents depreciation of special equipment. This equipment has no resale value and will be retained even if the product is outsourced.

$**$ Allocated FMOH and selling costs are corporate$-$level costs. The outsourcing decision is not expected to affect the total outflow on these accounts, over the decision$$s horizon.

Answer the following questions $($Each of the following parts is independent of the other parts.$)$

$1.$ Assume that the company has no alternative use for the facilities that are now being used to produce the carburetors. In the short$-$run, what is the effect on profit if the outside supplier$$s offer is accepted? Show all computations.

$2.$ What is the maximum volume level at which Troy Engines, Ltd$.,$ should outsource the carburetors $($i$.$e$.,$ decide to buy$)?$

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$3.$ Suppose that if the carburetors were purchased, Troy Engines, Ltd$.,$ would decrease its short$-$run profits by $$160,000$ per month. However, the firm could use the freed$-$up capacity to launch a new product. On a per unit basis, this new product would sell for $$15/$unit but costs $$14$ per unit to make. This cost of $$14$ per unit is made up of $($i$)$ the total inventoriable cost of $$9$ per unit which includes allocated fixed manufacturing costs of $$3$ per unit, and $($ii$)$ total selling costs of $$5$ per unit which includes fixed selling costs of $$1$ per unit. At what sales volume $($for the new product$)$ would it be profitable for Troy Engines Ltd$.,$ to purchase rather than make the carburetors? Show all computations.