Wing Sporting Goods $($WSG$)$ is a small company that makes two models of a metal baseball bat$$Sport and Collegiate. Both models are produced on a single machine. The price and costs of the two models are

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Sport Collegiate

Price per unit $ $285$ $ $470$

Variable cost per unit $ $108$ $ $188$

Machine minutes per unit $615$

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The one machine that is used to produce both models has a capacity of $35,100$ machine$-$minutes per quarter. Fixed manufacturing costs per quarter are $$445,000.$

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Required:

a$.$Suppose that the maximum unit sales in a quarter that WSG can achieve is $6,000$ units of each product. How many units of each model should WSG produce in a quarter?

b$.$Suppose that the maximum unit sales in a quarter that WSG can achieve is $4,200$ units of each product. How many units of each model should WSG produce in a quarter?