Sheffield's is the new favorite pizza, pasta, and sub place in town! Everyone raves about the generous portions and the delicious flavors of this restaurant's classic, go$-$to eats. After one year of operations, the manager, Laticia, wants to evaluate what has gone well and what could go better. She notes that while pizza represents the company's biggest sales volume item, it isn't necessarily the most profitable item. Alternatively, pasta, while not the biggest seller, does generate a very high contribution margin. Laticia is struggling with how to balance these two seemingly opposite products in terms of their profitability, while recognizing that subs are also becoming popular among the usual crowd. Here are the current contribution margins for each of the three products.

Contribution margin per unit $\frac{\text{P}\text{i}\text{z}\text{z}\text{a}}{\text{\$}6}\frac{\text{P}\text{a}\text{s}\text{t}\text{a}}{\text{\$}8}\frac{\text{S}\text{u}\text{b}}{\text{\$}4}$

Laticia knows that for every two sub sandwiches sold, Sheffield's sells three orders of pasta and five pizzas. She also knows that if she wants to keep her management position, and possibly even get another raise, she's going to have to help Sheffield's manage its growing costs. The operating costs, outside of the food costs, came to $$3,410$ last month. She has overheard the owner grumbling that this month and going forward, those costs are expected to increase.

$($b$)$

Recognizing that fixed costs are expected to increase, project a $20\%$ increase in fixed costs over last month, and determine a new break$-$even point in units for each of the three products. How many additional pizzas, pasta orders, and subs need to be sold just to cover the additional fixed costs?

Pizza units

Pasta units

Sub $$ units