I need help with the following problem, I got that to maximize total profit, the optimal prices would be:zoom Pro: $$3$ and zoom Business: $$5$ and the optimal strategy would be to sell both products. Can you please confirm? : Zoom has been approached by a UCSD start$-$up called EVT.ai$,$ which provides Zoom with EVT

$($EventVideoTagging$).$ EVT.ai does not only provide voice captioning but a whole solution, including AI$-$driven automatic video chaptering, table of contents, and learning tools.

Imagine that Zoom decides to implement EVT.ai solution into its business version product.

Together with other optional features, Zoom decides to sell the business version as $$Zoom Business.$$

On the other hand, Zoom also has a paid product version with relatively less advanced features,

branded $$Zoom Pro.$$ For simplicity, assume that Zoom only has these two versions of paid products

$($we ignore the free version and other paid versions.$)$

Zoom has done market research. Again, the market can be roughly seen as having two segments. In order to properly set a product and pricing strategy, the market research has to provide

information on consumer WTPs for each segment for the two versions of Zoom products, both

Zoom Pro and Zoom Business. The information is provided in the following table.

Zoom has to pay $$2$ for each copy of Zoom Business sold to EVT.ai and other providers.

However, all the features in Zoom Pro are built in$-$house, and there is no variable cost.

Zoom Pro Zoom Business

High$-$end Segment $(2$ million$)$ $$7$ $$12$

Low$-$end Segment $(3$ million$)$ $$3$ $$5$

$($a$)$ Consider that Zoom is going to sell both products, targeting Zoom Pro to the low$-$end segment

and Zoom Business to the high$-$end segment. The targeting has to be achieved by pricing: once a

price is set for each product, consumers are going to decide on their own what product to purchase

or whether to purchase at all. What would be the optimal prices for the two products? $($Hint:

we must also ensure that the high$-$end consumers will not purchase Zoom Pro, otherwise, only the

low$-$end Zoom Pro will be purchased, and the profit will suffer.$)$

$($b$)$ With both products, Zoom has a choice of product strategies. Zoom can sell one product or

sell and target both products to both segments. What would be the optimal strategy? $($Hint: you

still need to consider the optimal price for selling one product.$)$