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Question;PROBLEM;1. A snack food manufacturer buys corn for;tortilla chips from two cooperatives, one in Iowa and one in Illinois. The;price per unit of the Iowa corn is $5.50 and the price per unit of the Illinois;corn is $6.00.;a.;Define variables that would tell how many units to purchase from each;source.;b.;Develop an objective function that would minimize the total cost.;c.;The manufacturer needs at least 12000 units of corn. The Iowa;cooperative can supply up to 8000 units, and the Illinois cooperative must;supply at least 6000 units. Develop constraints for these conditions.;2. The relationship d = 5000- 25p describes what happens to demand (d);as price (p) varies. Here, price can vary between $10 and $50.;a.;How many units can be sold at the $10 price? How many can be sold at;the $50 price?;b.;Model the expression for total revenue.;c.;Consider prices of $20, $30, and $40. Which price alternative will;maximize total revenue? What are the values for demand and revenue at this;price?;3. There is a fixed cost of $50,000 to start a;production process. Once the process has begun, the variable cost per unit is;$25. The revenue per unit is projected to be $45.;a.;Write an expression for total cost.;b.;Write an expression for total revenue.;c.;Write an expression for total profit.;d.;Find the break-even point.;4. An author has received an advance against;royalties of $10,000. The royalty rate is $1.00 for every book sold in the;United States, and $1.35 for every book sold outside the United States. Define;variables for this problem and write an expression that could be used to;calculate the number of books to be sold to cover the advance.;5. A university schedules summer school courses;based on anticipated enrollment. The cost for faculty compensation;laboratories, student services, and allocated overhead for a computer class is;$8500. If students pay $420 to enroll in the course, how large would enrollment;have to be for the university to break even?;6. As part of their application for a loan to;buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast;operation, the prospective owners have projected;Monthly fixed cost (loan payment, taxes, insurance, maintenance);$6000;Variable cost per occupied room per night;$ 20;Revenue per occupied room per night;$ 75;a.;Write the expression for total cost per month. Assume 30 days per;month.;b.;Write the expression for total revenue per month.;c.;If there are 12 guest rooms available, can they break even? What;percentage of rooms would need to be occupied, on average, to break even?;7. Organizers of an Internet training session;will charge participants $150 to attend. It costs $3000 to reserve the room;hire the instructor, bring in the equipment, and advertise. Assume it costs $25;per student for the organizers to provide the course materials.;a.;How many students would have to attend for the company to break even?;b.;If the trainers think, realistically, that 20 people will attend, then;what price should be charged per person for the organization to break even?;8. In this portion of an Excel spreadsheet, the;user has given values for selling price, the costs, and a sample volume. Give;the cell formula for;a.;cell E12, break-even volume.;b.;cell E16, total revenue.;c.;cell E17, total cost.;d.;cell E19, profit/loss.;A;B;C;D;E;1;2;3;4;Break-even calculation;5;6;Selling price per unit;10;7;8;Costs;9;Fix cost;8400;10;Variable cost per unit;4.5;11;12;Break-even volume;13;14;Sample calculation;15;Volume;2000;16;Total revenue;17;Total cost;18;19;Profit loss;9. A furniture store has set aside 800 square;feet to display its sofas and chairs. Each sofa utilizes 50 sq. ft. and each;chair utilizes 30 sq. ft. At least five sofas and at least five chairs are to;be displayed.;a.;Write a mathematical model representing the store's constraints.;b.;Suppose the profit on sofas is $200 and on chairs is $100. On a given;day, the probability that a displayed sofa will be sold is.03 and that a;displayed chair will be sold is.05. Mathematically model each of the;following objectives;1.;Maximize the total pieces of furniture displayed.;2.;Maximize the total expected number of daily sales.;3.;Maximize the total expected daily profit.

Paper#57915 | Written in 18-Jul-2015

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