1.1 A manger of small firm is considering whether to produce a new product that would require leasing equipment at 20,000 per month. Also a production cost of $10 would be incurred each unit. Each unit would generate $20 revenue.
Develop a mathematical expression for monthly profits. Then determine how large this number needs to be each month to make it profitableto produce the product.
1.2 Management of the Toys R4US Company need to decide whether to introduce novelty toy to Christmas. Total cost required to produce is $50,000 plus $15 per toy produced. The Company would receive revenue of 35.00 for each toy.
A. Assuming every unit is sold, write expression for profit in terms and then find break-even point that number must exceed to make it worthwhile.
B. Now assumes that the number that can be sold might be less than number produced. Write expression for the profit in terms of these two numbers.
c. Formulate spreadsheet that will give profit in part b for any value of two numbers.
d. Write a mathematical expression for the constraint that the number produced should not exceed the number that can be sold.
2.1 Suppose that the estimates of the unit profits for the new products now have been revised to $600 for the doors and $300 for the windows.
a. Formulate and solve the revised linear programing model for this problem on spreadsheet.
b. Formulate same model algebraically.
c. Use the graphical method to solve this revised model.
3.1 Giacomi & Jackowitz suggests giving consideration to running commercials for Crunchy Start on nationally syndicated radio programs. Giacomi & Jackowitz estimates that cost of development each radio commercial would be $50,000. And exposures per commercial would be $90,000. The firm has determine that 10 spots are available or different radio commercials, and each one would cost $200,000 for normal run.
A. formulates and solve spreadsheet model for revised advertising mix-problem that includes this fourth advertising medium. Identify data cells, changing cells, and objective cell. Also show the Excel equation for each output cell expressed as a SUMPRODUCT function.
B. indicates why spreadsheet model is a linear programming model.
Express this model in algebraic form.
4.1
Reboot Inc. is a manufacture of hiking boots. The demand next year is expected to be 3,000, 4,000, 8,000, and 7,000 pair of boots in quarters 1, 2, 3, and 4 respectively. With its current production facility the company can produce at most 6,000 pairs of boots in any quarter. Each pair sold generates a profit of $20 per pair. Each pair at end of quarter incurs $8 in storage and capital recovery cost. Reboots has 1,000 pair of boots in inventory at the start of quarter 1. Reboot top management has given you the assignment of doing some spread sheets modeling to analyze what the product schedule should be the next four quarters and make a recommendation.
a. Visualize where you want to finish. What numbers will top management need whatdecision needs to be made? What should the objective be?
b. Suppose the reboot were produced 5,000 pairs of boots in each of the first two quarters. Calculate by hand the ending inventory, profit from sales, and inventory cost for quarters 1 and 2.
c. Make a rough sketch of a spreadsheet model, with blocks laid out for the data cells, changing cells, output cells, and objective cell.
d. builds a spreadsheet models for 1 and 2, and then thoroughly test model.
e. Expand the model to full scale and then solve it.