The research department at a manufacturing company has developed a new process that it believes will result in an improved product. Management must decide whether to go ahead and market the new product. The new product may or may not be better than the old one. If the new product is better and the company decides to market it, sales should increase by \( \$ 50,000 \). If it is not better and they replace the old product with the new product on the market, they will lose \( \$ 22,000 \) to competitors. If they decide not to market the new product, they will lose a total of \( \$ 30,000 \) if it is better and just research costs of \( \$ 10,000 \) if it is not. Complete parts (a) and (b) below. (a) Prepare a payoff matrix. (Type an integer or decimal for each matrix element. Do not include the \( \$ \) symbol in your answer.)

To prepare a payoff matrix for the scenario involving the new product, we can outline the decisions and potential outcomes as follows: 1. **Decisions**: - Market the new product - Do not market the new product 2. **Outcomes** (regarding the new product): - New product is better - New product is not better Now we can build the payoff matrix based on the provided information: | | New Product is Better | New Product is Not Better | |-------------------------------|-----------------------|---------------------------| | Market the New Product | 50000 | -22000 | | Do Not Market the New Product | -30000 | -10000 | In this matrix: - If the new product is better and they market it, they gain $50,000. - If they market it and the product is not better, they lose $22,000. - If they do not market it and the product is better, they lose $30,000. - If they do not market it and the product is not better, they lose $10,000 (just the research cost).