1. The relationship d = 5000 - 25p describes what happens to demand (d) as price (p) varies. Price can vary between $10 and $50. How many units can be sold when the price is $10? 2. Administrators at a university are planning to offer a summer seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? 3. Students are organizing a "Battle of the Bands" contest. They know that at least 100 people will attend. The rental fee for the hall is $150 and the winning band will receive $500. In order to guarantee that they break even, how much should they charge for each ticket? 4. A production process requires a fixed cost of $50,000 and the variable cost per unit is $25. The revenue per unit was projected to be $45, but a recent marketing study shows that because of an emerging competitor, the revenue will be about 12% lower. How does this affect the break-even point? 8. The College Coffee Cafe buys tea from three suppliers. The price per pound is $15.00 from supplier A, $17.50 from supplier B, and $21.00 from supplier C. They have budgeted $175 to purchase the tea. The cafe needs at least 12 pounds of tea, and supplier C can supply no more than 4 pounds. Develop constraints for these conditions. 9. The College Coffee Cafe receives a profit of $1.25 for each cup of house tea that they sell, $1.40 for each cup of the premium brand, and $1.50 for each cup of their special blend. Develop an objective that maximizes profit. 10.A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is $6 from cooperative A and $5.50 per unit from cooperative B. The manufacturer needs at least 12,000 units of peas. Cooperative A can supply up to 8000 units, and cooperative B can supply at least 6000 units. 5. A popular performer is scheduled to appear at a major city. The promoter is deciding between two venues, the larger of which costs $20,000 to rent and the smaller of which costs $12,000 to rent. Ticket prices for the smaller venue are $20, but the promoter is unsure what to charge per ticket for the larger venue. If exactly 1000 customers arrive, what percentage change in ticket prices would make the profit at the large venue identical to that of the smaller venue? 6. A newly opened bed-and-breakfast projects the following: Monthly fixed costs $8000 Variable cost per occupied room per night $40 Revenue per occupied room per night $165 Write the expression for total cost per month. Write the expression for total revenue per month. How many rooms would have to be occupied per month in order to break even? 7. A group of professors struggles to craft a set of assessment questions for their operations management intro class. They want to cover four topic areas with at least four questions each and have no more than twenty questions total for the assessment. What would a set of constraints look like if they chose an optimization approach to the assessment