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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UpStudy AI · Accepted Answer

Let $$ p = 0.4 $$ be the probability that the new product is better, and $$ 1-p = 0.6 $$ the probability that it is not.

**Step 1. Calculate the expected profit if the product is marketed.**

- If the new product is better, the profit is $$ \$50,\!000 $$.
- If it is not better, the loss is $$ \$22,\!000 $$, i.e. profit $$ -\$22,\!000 $$.

Thus, the expected profit when marketing is
$$
E[\text{market}] = 0.4(50,\!000) + 0.6(-22,\!000).
$$
Calculate each part:
$$
0.4 \times 50,\!000 = 20,\!000,
$$
$$
0.6 \times (-22,\!000) = -13,\!200.
$$
So,
$$
E[\text{market}] = 20,\!000 - 13,\!200 = 6,\!800.
$$

**Step 2. Calculate the expected profit if the product is not marketed.**

- If the new product is better, the loss is $$ \$30,\!000 $$, i.e. profit $$ -\$30,\!000 $$.
- If it is not better, the loss is only the research cost of $$ \$10,\!000 $$, i.e. profit $$ -\$10,\!000 $$.

Thus, the expected profit when not marketing is
$$
E[\text{not market}] = 0.4(-30,\!000) + 0.6(-10,\!000).
$$
Calculate each part:
$$
0.4 \times (-30,\!000) = -12,\!000,
$$
$$
0.6 \times (-10,\!000) = -6,\!000.
$$
So,
$$
E[\text{not market}] = -12,\!000 - 6,\!000 = -18,\!000.
$$

**Step 3. Compare the strategies.**

- Expected profit if marketing: $$ \$6,\!800 $$
- Expected profit if not marketing: $$ -\$18,\!000 $$

Since $$ \$6,\!800 > -\$18,\!000 $$, the best action is to market the product.

**Final Answer:**

D. The expected profits are $$ \$6,\!800 $$ if they market the product and $$ -\$18,\!000 $$ if they do not. They should market the product because they will earn more if they do so.
They should market the product because earning \$6,800 is better than losing \$18,000.

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