We produce our radar sensors for autonomous vehicles in two different plants, and I would like you to think about optimal production levels in our multi-plant production scheme to maximize our profits.

Ourfirst plant has the following weekly cost structure: C₁(Q₁)= 20,000 + 0.5Q₁² and oursecond plant has the following weekly cost structure: C₂(Q₂) = 40,000 + 0.25Q₂².

Furthermore, our sales team has informed me that our weekly inverse demand function takes the following form: P(Q) = 500 - 0.5Q.

Give me a recommendation on what weekly production levels should be in each plant, and also recommend a price point for us to hit our sales target. Finally, let me know what our forecasted profits will be if we follow your production and pricing advice.