A Company Sells Three Products as Shown Below These Three Products All Always Sold in Fixed Proportions

A company sells three products as shown below: $$\begin{array} { | l | r | r | r | r | } \hline & \text { Product X} & \text { Product Y} & \text { Product Z} & \text { Total } \\\hline \text { Units } & 60,000 & 140,000 & 50,000 & 250,000 \\\hline \text { Sales } & \$ 90,000 & \$ 150,000 & \$ 60,000 & \$ 300,000 \\\hline \text { Variable Costs } & \$ 63,000 & \$ 93,000 & \$ 19,000 & \$ 175,000 \\\hline \begin{array} { l } \text { Contribution } \\\text { Margin }\end{array} & & & & \$ 125,000 \\\hline \text { Fixed Costs } & & & &\$100,000 \\\hline\end{array}$$ These three products all always sold in fixed proportions. In other words, Product X always accounts for 24% of total sales (60,000/250,000), Product Y always accounts for 56% of total sales (140,000/250,000), and Product Z always accounts for 20% of total sales (50,000/250,000).
Required:
a. How many units of each product need to be sold to break-even?
b. How many units must of each product must be sold if the company wants to have a profit of $50,000?