The Scottie Sweater Company produces sweaters under the $$Scottie$$ label. The company buys raw wool and processes it into wool yarn from which the sweaters are woven. One spindle of wool yarn is required to produce one sweater. The costs and revenues associated with the sweaters are given below:

Per Sweater

Selling price $ $41\mathrm{.}00$

Cost to manufacture:

Raw materials:

Buttons, thread, lining $ $2\mathrm{.}00$

Wool yarn $20\mathrm{.}00$

Total raw materials $22\mathrm{.}00$

Direct labor $8\mathrm{.}40$

Manufacturing overhead $12\mathrm{.}6043\mathrm{.}00$

Manufacturing profit $($loss$)$ $ $(2\mathrm{.}00)$

Originally, all of the wool yarn was used to produce sweaters, but in recent years a market has developed for the wool yarn itself. The yarn is purchased by other companies for use in production of wool blankets and other wool products. Since the development of the market for the wool yarn, a continuing dispute has existed in the Scottie Sweater Company as to whether the yarn should be sold simply as yarn or processed into sweaters. Current cost and revenue data on the yarn are given below:

Per Spindle of Yarn

Selling price $ $28\mathrm{.}00$

Cost to manufacture:

Raw materials $($raw wool$)$ $ $11\mathrm{.}00$

Direct labor $3\mathrm{.}60$

Manufacturing overhead $5\mathrm{.}4020\mathrm{.}00$

Manufacturing profit $ $8\mathrm{.}00$

The market for sweaters is temporarily depressed, due to unusually warm weather in the western states where the sweaters are sold. This has made it necessary for the company to discount the selling price of the sweaters to $$41\mathrm{.}00$ from the normal $$51\mathrm{.}00$ price. Since the market for wool yarn has remained strong, the dispute has again surfaced over whether the yarn should be sold outright rather than processed into sweaters. The sales manager thinks that the production of sweaters should be discontinued; she is upset about having to sell sweaters at a $$2\mathrm{.}00$ loss when the yarn could be sold for a $$8\mathrm{.}00$ profit. However, the production superintendent does not want to close down a large portion of the factory. He argues that the company is in the sweater business, not the yarn business, and the company should focus on its core strength.

All of the manufacturing overhead costs are fixed and would not be affected even if sweaters were discontinued. Manufacturing overhead is assigned to products on the basis of $150\%$ of direct labor cost. Materials and direct labor costs are variable.

Required:

$1.$ What is the financial advantage $($disadvantage$)$ of further processing one spindle of wool yarn into a sweater?

$2.$ Would you recommend that the wool yarn be sold outright or processed into sweaters?

$3.$ What is the lowest price that the company should accept for a sweater?