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. Our first plant has the following weekly cost structure: C1(Q1)= 20,000 + 0.5Q12 and our second 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.