We produce our radar sensors for autonomous vehicles in two different plants, and I would like...

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.

Expert Solution

In this question we have to combine the costs and then calculate total revenue and do the question by differenciation as seperate demand curves are not given. the price for the product will be

500-Q1-Q2 which is $125/unit.

and quantity produced are

Q1= 125units and Q2= 250units

Rahul Sunny answered 2 years ago

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