1. (12 points) Three production processes, A, B, and C have the following cost structure: Process Fixed Cost Per Year Variable Cost Per Unit A $120000 $3.0 B $90000 $4.0 C $80000 $4.5 (1) (4 points) What is the most economical process for a volume of 8000 units?

(2) (4 points) How many units per year must be sold with each process to have annual profits of $50000 if the selling price is $6.95 per unit? (3) (4 points) What is the break-even volume for each process? 2. (13 points) Sales (in thousands) of the new Thorton Model 506 convection oven over the eight-week period since its introduction have been as follows: Week 1 2 3 4 5 6 7 8 Sales 18.6 21.4 25.2 22.4 24.6 19.2 21.7 23.8 Which exponential smoothing model provides better forecasts, one using = 0.6 or = 0.2? Compare them using mean squared error.

3. (30 points) Temax realtor company advertises for its business through television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Television Radio Online Audience per advertisement 100000 18000 40000 Cost per advertisement 1800 300 600 Maximum media usage 12 16 12 To ensure a balanced use of advertising media, radio advertisements must not exceed 40% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. 1. If the promotional budget is limited to $17600, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media, and what is the total audience reached? (Dont worry if your answer is in decimals). 2. By how much would audience contact increase if an extra $100 were allocated to the promotional budget?

4. (20 points) The Northwest Flower Company owns a greenhouse, which furnishes roses and carnations to florists in Oregon, Washington, and Idaho. The greenhouse can grow any combination of the two flowers. They sell the flowers in bunches with 25 blooms to a bunch. They have 10000 square feet available for planting this year. Each bunch of roses takes about 4 square feet and each bunch of carnations about 5 square feet. Special fertilizer is required for flowers: roses need 3 pounds and carnations 2 pounds. The availability of the fertilizer is limited to 5000 pounds. Sales commitments require the company to grow at least 500 bunches of roses. Profit contributions are $6 per bunch of roses and $8 per bunch of carnations. LP Problem is given by X1 : the number of rose bunches planted. X2 : the number of carnation bunches planted. max 6X1 + 8X2 4X1 + 5X2 10000 3X1 + 2X2 5000 X1 500 (1) (8 points) Plot the feasible region on desmos. Download the image and then embed the image in excel document. (2) (7 points) What are the corner points of the feasible region. (3) (5 points) What is the optimal solution and the optimal value of objective function?

5. (25 points) Yorktown Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Yorktown needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y carpet uses 40 units of synthetic fiber, requires 28 hours of production time, and needs 15 units of foam backing. The profit per roll of Grade X carpet is $200 and the profit per roll of Grade Y carpet is $160. In the coming production period, Yorktown has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility). The company has 1500 units of foam backing available for use. Develop and solve a linear programming model for this problem.