Consider again the Windbreakers firmdescribed in the text. Suppose that Windbreakers determines that dropping the Gale product line will release production capacity so that it can manufacture additional units of Windy. Assume that, asdescribed in the text, the two production constraints are the automated sewing machine and the inspection and packaging operation. The automated sewing machine can make 20 Windys or 30 Gales per hour. As before, the inspectionand packaging operation requires 15 minutes for a Windy (4 per hour) and 5 minutes for a Gale (12 per hour). The unit margin contribution of Windy and Gale is $8 and $4 respectively. Currently, 3,840 Gales and 18,750 Windys are being manufactured and sold. (Disregard whether this current solution is optimal.) Sales projections, determined on the basis of recent marketing analysis, show that sales of Windy could be increased to 30,000 units if additional capacity were available.

Required:

1. If Windbreakers deletes Gale entirely, how many units of Windy can it manufacture solely because of the the capacity released by discontinuing the production of Gale?

2. What is the dollar effect on operating income if Windbreakers drops the production and sale of Gale and uses the resulting released capacity--and only this released capacity--for Windy?

Case 2: Two or More Production Constraints When there are two or more production constraints, the choice of sales mix involves a more complex analysis, and in contrast to the case of one production constraint (in which the optimum solution will include only a single product, assuming sufcient demand for this productsee Exhibit 11.19), the solution can include both products when two constraints are involved. To continue with the Windbreakers case, assume that in addition to the use of sewing machine time, a second production activity is required. The second activity inspects and packages the completed product. This operation is done by 40 workers, each of whom can complete the operation for the Windy jacket in 15 minutes and for the Gale jacket in 5 minutes (because of differences in material quality, less inspection time is required for the Gale jacket). This means that 4 (60 min.,! 15 min.) Windy jackets or 12 Gale {60 min.;'5 min.) jackets can be inspected and packaged in an hour. 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 40hour week, which means 35 hours of actually performing the operation, given time for breaks, training, and other tasks. Thus, 5,600 hours (40 workers x 35 hours/week x 4 weeksfmonth) are available per month for the inspection and packaging activity. The maximum output per month for the Windy jacket, in terms of inspection and packaging activity, is 22,400 (5,600 hours x 4 jackets per hour). Similarly, the maximum output for the Gale jacket is 67,200 (5,6000 hours x 12 jackets per hour). All of this information is summarized in Exhibit 1 1. 20 EXHIBIT 11.20 Windbreakers Data for the Windy and Gale Plant: The Second Constraint--Inspection and Packaging Activity Windy Gale Given: Contribution margin per jacket $8 $4 Inspection and packaging time per jacket 15 min. 5 min. Then: Number of jackets per hour 4 12 Contribution margin per labor hour (4 jackets per hour x $8 per jacket; 12 jackets per hour x $4 per jacket) $32 $48 Also: The maximum monthly production for each product, given the 5,600-hour constraint: For Windy: 5,600 hours/month x 4 jackets per hour 22,400 For Gale: 5,600 hours/month x 12 jackets per hour 67,200 Windbreakers Production and Sales Possibilities EXHIBIT 11.21 (Feasible Area): Two Production Constraints-Sewing Machine and Inspection / Packaging Activity 67,200 Production constraint for inspection and packaging activity Monthly Sales, Gale Feasible area 36,000 Production constraint for sewing machine time Point A (4,800 Gale, 20,800 Windy) 24,000 22,400 Monthly Sales, WindyThe production possibilities for two constraints are illustrated in Exhibit 11.21 . In addition to the production possibilities for machine time, we show the production possibilities for the inspection and packaging activity. The darker shaded area indicates the range of possible outputs (the "feasible area") for both Gale and Windy. Note that it is not possible to produce more than 22,400 units of Windy because all 40 workers inspecting and packaging full-time would not be able to handle more than that number, even though sufficient sewing machine time is available for producing 24,000 units. That is, production of more than 22,400 units of Windy is outside of the feasible area. Similarly, although Windbreakers could pack and ship 67,200 units of Gale by having all 40 individuals work full-time on this jacket, the firm could manufacture only 36,000 units of Gale because of limited capacity on the sewing machines. We can determine the best production mix by examining all of the possible production possibilities in the darker shaded area, from 36,000 on the Gale axis to point A where the constraints intersect, and then to the point 22,400 on the Windy axis. The sales mix with the highest contribution must be one of these three points: 36,000 units of Gale, point A (20,800 units of Windy and 4,800 units of Gale), or 22,400 units of Windy. The optimal solution, called the corner point analysis, is obtained by finding the total contribution margin at each point and then choosing the point with the highest total contribution margin. The solution achieved in this manner is for production at point A: 20,800 units of table: Windy and 4,800 units of Gale.2 A summary analysis of the three production possibilities is presented in the following Total Contribution Corner Point Windy Gale Margin O $ O 0 36,000 144,000 22,400 179,200 20,800 4,800 $185,600 One way to see why point A represents an optimum short-term product mix is to impose on Exhibit 11.21 an iso- profit line, whose negative slope is equal to the ratio of the unit contribution margin of Gale to the unit contribution margin of Windy (i.e., -2.0). Extend this line to the right, from the origin until it just touches a point in the feasible region. This particular iso-profit line determines the optimum profit given the stated constraints and product in Exhibit 11.21 contribution margins. Once again, you will see that the optimum short-term product mix is indicated by point A