ABC Manufacturing is planning to build a new plant to manufacture a newly developedproduct. The company is trying to decide between building a small, medium, or large plant,depending on the demand for the product. The profit per year will depend on the marketdemand which could be low, medium, or high. The estimated profits for each scenario havebeen developed by the company’s Planning and Financial Analysis Division. All $ are inthousands..Market DemandSize of Plant Low Medium HighSmall 300 400 400Medium 100 500 500Large – 400 100 900What decision should be made according to the following decision rules? (show work)(a) Maximax (Optimistic)(b) Maximin (Pessimistic)(c) LaPlace(d) minimax regret(e) Suppose a market researcher with expertise in the introduction of new products estimatedprobabilities of low, medium, and high demand for this particular type of product to be0.3, 0.5, and 0.2 respectively. What decision should be made with this new information?