Garett Engines Ltd$.($GEL$)$ manufactures a variety of engines for use in heavy equipment. The company has always produced all of the necessary parts for its engines, including all of the oil pumps. An outside supplier has offered to produce and sell one type of oil pump to GEL for a cost of $$41$ per unit. To evaluate this offer, GEL has gathered the following information relating to its cost of producing $15,600$ oil pumps:

Direct materials cost $$20$ per unit.

GEL pays its direct labour employees $$20$ per hour; each oil pumps requires $30$ minutes of labour time.

Variable manufacturing overhead is allocated at $30\%$ of direct labour cost.

Total fixed manufacturing cost amounts to $$15$ per unit, of which $60\%$ is allocated common cost and the remaining $40\%$ covers depreciation of special equipment and supervisory salaries. The special equipment has no resale value. Supervisory personnel will be transferred to a different department if the company decides to purchase the oil pump from the outside supplier.Garett Engines Ltd$.($GEL$)$ manufactures a variety of engines for use in heavy equipment. The company has always produced all of the necessary parts for its engines, including all of the oil pumps. An outside supplier has offered to produce and sell one type of oil pump to GEL for a cost of $$41$ per unit. To evaluate this offer, GEL has gathered the following information relating to its cost of producing $15,600$ oil pumps:

Direct materials cost $$20$ per unit.

GEL pays its direct labour employees $$20$ per hour; each oil pumps requires $30$ minutes of labour time.

Variable manufacturing overhead is allocated at $30\%$ of direct labour cost.

Total fixed manufacturing cost amounts to $$15$ per unit, of which $60\%$ is allocated common cost and the remaining $40\%$ covers depreciation of special equipment and supervisory salaries. The special equipment has no resale value. Supervisory personnel will be transferred to a different department if the company decides to purchase the oil pump from the outside supplier.Suppose that, if the oil pump were purchased, GEL could use the freed capacity to launch a new product. The segment margin of the new product would be $$150,000$ per year. Compute the total differential cost for producing and buying the product.