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 ket 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 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 nof to market the new product, they will lose a total 30,000 if it is better and just research costs of \( \$ 10,000 \) if it is not. Complete parts (a) and (b) below. If management believes that the probability that the new product is better is 0.4 , find the expected profits under each strategy and determine the best action. elect the correct answer below and fill in the answer boxes to complete your choice. ype integers or decimals.) A. The expected profits are \( \$ ~ i f ~ t h e y ~ m a r k e t ~ t h e ~ p r o d u c t ~ a n d ~ \) B. if they do not. They should not market the product because they will earn more if they do not. B. The expected profits are \( \$ \square \) if they market the product and \( \$ \square \) if they do not. They should not market the product because they will lose less if they do not. C. The expected profits are \( \$ \square \) if they market the product and \( \$ \square \) if they do not. They should market the product because they will lose less if they do. D. The expected profits are \( \$ \square \) if they market the product and \( \$ \square \) if they do not. They should market the product because they will earn more if they do so.
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To determine the expected profits, we can calculate them under each strategy based on the given probabilities and outcomes. If they market the new product: - Probability that the new product is better: \( 0.4 \) - Probability that the new product is not better: \( 0.6 \) (since \( 1 - 0.4 = 0.6 \)) - Expected profit if the product is better: \( \$50,000 \times 0.4 = \$20,000 \) - Expected loss if the product is not better: \( -\$22,000 \times 0.6 = -\$13,200 \) - Total expected profit if they market the product: \( 20,000 - 13,200 = \$6,800 \) If they do not market the new product: - Loss if the product is better: \( -\$30,000 \) (since they lost out on the potential product) - Loss if the product is not better: \( -\$10,000 \) (just research costs) - Total expected loss if they do not market: \( -30,000 \times 0.4 - 10,000 \times 0.6 = -12,000 -6,000 = -18,000 \) So, we summarize: A. The expected profits are \( \$6,800 \) if they market the product and \( -\$18,000 \) if they do not. B. They should market the product because they will earn more if they do so. The correct choice is D.
