Wow Chemical Canada Inc. produces three products at its plant in North San JoseAlpha, Beta, andGamma. Their selling prices and costs per barrel are as follows:

Alpha Beta Gamma

Selling price $ 116 $ 125 $ 160

Direct materia 32 40 38

Direct labour (@ $20 per hour) 20 30 40

Variable overhead 16 23 32 Variable selling 2 2 3 Total variable costs 70 95 113 Fixed overhead * 13.50 20.25 27 The plants total fixed costs are $1,632,000 per year (i.e., the fixed overhead of $1,215,000 plusplant-specific fixed selling and administrative costs of $417,000).

The marketing department forecasts that, next year, the plant could sell a maximum of 50,000 barrelsof each product. The plants constrained resource is direct labor hours. Practical capacity is 90,000direct-labor hours per year Determine the optimal sales mix: How many barrels of each productshould the plant produce to maximize its profit? [Show all necessary calculations.]