Introduction to Management Science
1) A production process requires a fixed cost of $50,000. The variable cost per unit is $25 and the revenue per unit is projected to be $45. Write a mathematical expression for total profit.
2) A production process requires a fixed cost of $50,000. The variable cost per unit is $25 and the revenue per unit is projected to be $45. Find the break-even point.
3) 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?
4) Administrators at a university will charge students $150 to attend a 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. How many students would have to register for the seminar for the university to break even?
5) 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?
6) 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 30 students pay $175 for the privilege of attending the seminar, how much of a profit (or loss) will be incurred?
7) 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.
8) 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 revenue per month.
9) 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
How many rooms would have to be occupied per month in order to break even?
10) A script writer has received an advance against royalties of $10,000. The royalty rate is $2 for every performance in the U.S., and $3 for every performance outside the U.S. Define variables for this problem.
61) A business analyst describes his company's profit function as 3x2 + 6x - 200. If x is the output volume, what statements can you make about the price, fixed cost, and variable cost?
11) A script writer has received an advance against royalties of $10,000. The royalty rate is $2 for every performance in the U.S., and $3 for every performance outside the U.S. Write an expression that could be used to compute the number of performances in order to cover the advance.
12) 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?
13) 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?
14) 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. Define variables that would tell how many units to purchase from each source.
15) 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. Develop an objective function that would minimize the total cost.
16) 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. Develop constraints for these conditions.
17) 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?
18) What are some different types of decision support systems?
19) A manager of the cereal bar at the college campus has determined that the profit made for each bowl of Morning Buzz cereal sold, x, is equal to: Z = $4x - 0.5x. Each bowl of Morning Buzz weighs 6 ounces, and the manager has 12 lbs (192 ounces) of cereal available each day, which can be written as the constraint, 6x ≤ 192. What maximum profit will be made from Morning Buzz if it is all sold in one day?
20) The College Coffee Café 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 caféneeds at least 12 pounds of tea, and supplier C can supply no more than 4 pounds. Develop constraints for these conditions.
21) The College Coffee Café 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.
22) The steps of the management science process are:
A) problem definition, model construction, observation, model solution, implementation.
B) observation, problem definition, model construction, model solution, implementation.
C) model construction, problem definition, observation, model solution, implementation.
D) observation, implementation, problem definition, model construction, model solution.
23) A model is a functional relationship that includes:
A) variables.
B) parameters.
C) equations.
D) all of the above
24) Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model?
A) a decision variable
B) an objective function
C) a constraint
D) a parameter