Your Lego furniture company makes Tables and Chairs. Below, you are given the starting inventory, selling price, and Bill of Materials (recipe, or construction requirements). You are to determine the number of Tables and Chairs to be built to maximize revenue. You must make 4 chairs for every table. Your answer will be the revenue generated by your production plan - rounded to the nearest whole dollar. (The number of tables and chairs must be a whole number.) Scenario 1 Large wood per table 3 Small wood per table 2 Large wood per chair 1 Small wood per chair 4 Revenue per table $35 Revenue per chair $29 Large wood inventory 300 Small wood inventory 500

Your Lego furniture company makes Tables and Chairs. Below, you are given the starting inventory, selling price, and Bill of Materials (recipe, or construction requirements). You are to determine the number of Tables and Chairs to be built to maximize revenue. You must make 4 chairs for every table. Your answer will be the revenue generated by your production plan - rounded to the nearest whole dollar. (The number of tables and chairs must be a whole number.) Scenario 1 Large wood per table 3 Small wood per table 2 Large wood per chair 1 Small wood per chair 4 Revenue per table $35 Revenue per chair $29 Large wood inventory 300 Small wood inventory 500

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 83P

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If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).
Suppose you begin year 1 with 5000. At the beginning of each year, you put half of your money under a mattress and invest the other half in Whitewater stock. During each year, there is a 40% chance that the Whitewater stock will double, and there is a 60% chance that you will lose half of your investment. To illustrate, if the stock doubles during the first year, you will have 3750 under the mattress and 3750 invested in Whitewater during year 2. You want to estimate your annual return over a 30-year period. If you end with F dollars, your annual return is (F/5000)1/30 1. For example, if you end with 100,000, your annual return is 201/30 1 = 0.105, or 10.5%. Run 1000 replications of an appropriate simulation. Based on the results, you can be 95% certain that your annual return will be between which two values?
Another way to derive a demand function is to break the market into segments and identify a low price, a medium price, and a high price. For each of these prices and market segments, we ask company experts to estimate product demand. Then we use Excels trend curve fitting capabilities to fit a quadratic function that represents that segments demand function. Finally, we add the segment demand curves to derive an aggregate demand curve. Try this procedure for pricing a candy bar. Assume the candy bar costs 0.55 to produce. The company plans to charge between 1.10 and 1.50 for this candy bar. Its marketing department estimates the demands shown in the file P07_47.xlsx (in thousands) in the three regions of the country where the candy bar will be sold. What is the profit-maximizing price, assuming that the same price will be charged in all three regions?
In the cash balance model from Example 11.5, the timing is such that some receipts are delayed by one or two months, and the payments for materials and labor must be made a month in advance. Change the model so that all receipts are received immediately, and payments made this month for materials and labor are 80% of sales this month (not next month). The period of interest is again January through June. Rerun the simulation, and comment on any differences between your outputs and those from the example.

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	Scenario 1
Large wood per table	3
Small wood per table	2
Large wood per chair	1
Small wood per chair	4
Revenue per table	$35
Revenue per chair	$29
Large wood inventory	300
Small wood inventory	500