Two Production Constraints; Corner Point Analysis; Linear Programming $($Appendix$)$ Let us

revisit the Windbreakers Inc. situation from the chapter. Information from Exhibit $11\mathrm{.}16$B is reproduced

below and shows the results after Gale was dropped and the avoidable marketing expenses

were also removed.

Calm Windy Total

Sale in units $25,00018,750$

Sales $($$$30$ and $$32$ per unit$)$ $$750,000$ $$600,000$ $$1,350,000$

Variable cost $($$$24$ per unit$)600,000450,0001,050,000$

Contribution margin $$150,000$ $$150,000$ $ $300,000$

Traceable Advertising $25,00015,00040,000$

Contribution after all relevant costs $$125,000$ $$135,000$ $ $260,000$

Fixed cost $($unavoidable$)$ $ $111,000$

Operating profit $ $149,000$

We will now assume that the production of the remaining products, Calm and Windy, requires

an automated sewing machine to stitch the jackets and that this production activity is a limited

resource: Sales demand for the two products exceeds the capacity of the plant$$s three automated sewing

machines. Each machine can be run up to $20$ hours per day five days per week, or $400$ hours per

month, which is its maximum capacity allowing for maintenance. This gives $1,200(3$ machines $\backslash$times

$400$ hours per machine$)$ available hours for sewing each month. Assume further that the machine

requires four minutes to assemble a Calm and three minutes to assemble a Windy.

A second activity inspects and packages the completed product, and this operation is done by

$40$ workers. Because of the limited size of the facility, no more than $40$ workers can be employed

effectively in the inspection and packaging process. These employees work a $40-$hour week, which

means $35$ hours of actually performing the operation, given time for breaks, training, and other tasks.

Thus, $5,600$ hours $(40$ workers $\backslash$times $35$ hours$/$week $\backslash$times $4$ weeks$/$month$)$ are available per month for the

inspection and packaging activity. While the workers can complete the activity for the Calm jacket in

$6$ minutes, due to its heavier weight and the insulation, it takes the workers $15$ minutes to complete

the operation for the Windy jacket.

Required

$1.$ Determine the contribution margin per hour, the maximum production per month, and the maximum

contribution per month for each product if the sewing machines were the only constraining resource.

From a strictly financial perspective, which product would you recommend Windbreakers produce?

$2.$ Determine the contribution margin per hour, the maximum production per month, and the maximum

contribution per month for each product if the inspection and packing activity were the only constraining

resource. From a strictly financial perspective, which product would you recommend Windbreakers

produce?

$3.$ Recognizing there are two constraining resources, management decides to do a further analysis. Graph

the maximum production results from requirements $1$ and $2$ and do a corner point analysis. For this

requirement, ignore the avoidable fixed costs.