An artist travels to craft fairs all summer long. She must book her booth at a June craft show six months in advance and decide if she wishes to rent a tent for an extra \( \$ 425 \) in case it rains on the day of the show. If it does not rain, she believes she will earn \( \$ 3100 \) at the show. If it rains, she believes she will earn only \( \$ 2100 \), provided she has a tent. If she does not have a tent and it does rain, she will have to pack up and go home and will thus earn \( \$ 0 \). Weather records over the last 10 years indicate there is a 0.4 probability of rain in June. Complete parts (a) and (b). (a) Prepare a profit matrix. (Do not include the \( \$ \) symbol in your answer.)

To prepare a profit matrix for the artist’s decision-making process, we will first calculate the profits based on two scenarios: renting a tent and not renting a tent. Then, we will factor in the costs and the probabilities of rain. Let's lay out the possible profits: 1. **If the artist rents a tent**: - If it rains (probability = 0.4): Earnings = \( \$ 2100 \) - \( \$ 425 \) = \( \$ 1675 \) - If it does not rain (probability = 0.6): Earnings = \( \$ 3100 \) - \( \$ 425 \) = \( \$ 2675 \) 2. **If the artist does not rent a tent**: - If it rains (probability = 0.4): Earnings = \( \$ 0 \) - If it does not rain (probability = 0.6): Earnings = \( \$ 3100 \) Now we can present this in a profit matrix format: | | Rains (0.4) | Does Not Rain (0.6) | |----------------|-------------|----------------------| | **Rents Tent** | 1675 | 2675 | | **Does Not Rent Tent**| 0 | 3100 | This matrix helps the artist visualize her potential profits based on the weather outcomes and whether she chooses to rent a tent or not.