Problem 1: Production Planning: Ebel Mining Company owns two different mines that produce a given kind of ore. After crushing, ore is one of three grades: high, medium or low. Ebel must provide the parent company with at least 12 tons of high grade, 8 tons of medium grade, and 24 tons of low-grade ore per week. It costs $20,000 a day to run the first mine and $16,000 a day to run the second mine. In one day each mine produces the following tonnage: Mine 1 Mine 2 High 6 2 Medium 2 2 Low 4 12 How can Ebel meet the requirements of the parent company at the lowest cost? Formulate a linear program. Problem 2: The Colorado Cattle Company*: The Colorado Cattle Company (CCC) can purchase three types of raw feed ingredients from a wholesale distributor. The company's cattle have certain nutritional requirements with respect to fat, protein, calcium and iron. Each cow requires at least 10 units of calcium, no more than 7.5 units of fat, at least 12 units of iron and at least 15 units of protein per day. The table below shows the amount of fat, protein, calcium and iron in each pound of the three feed ingredients. Grade 1 feed costs $.25, grade 2, $.10, and grade 3, $.08 per pound. The cattle can be fed a mixture of the three types of raw feed. CCC would like to feed its herd as cheaply as possible. Page 1 of 2 Feed Ingredients (Units Per Pound) Grade 1 Grade 2 Grade 3 Calcium .7 .8 0 Iron .9 .8 .8 Protein .8 1.5 .9 Fat .5 .6 .4 Formulate the problem and solve it using Excel Solver. What if the costs were $.5, $.75, and $.2 per pound? What if each cow required 20 units of calcium? Problem 3 True or False: The following is a linear program. Min st. x1+x2 x1 < 1 x2 < 1 x1 ≥0 x2 ≥0 Problem 4: An automobile manufacturer produces several kinds of cars. Each kind requires a certain amount of factory time per car to produce, and yields a certain profit per car. A certain amount of factory time has been scheduled for next week, and it is desired to use all of this time; but at least a number of each kind of car must be manufactured to meet dealer requirements. (a) Suppose there are three kinds of cars, known as T, C, and L with the following times to produce per car, profit per car, and dealer orders for each car. Car time T 1 C 2 L 3 profit 200 500 700 orders 10 20 15 Maximum number of production hours = 120 i. What are the decision variables for this problem? ii. Write this problem as a linear program that maximizes profit. (b) How could you generalize this model for a problem with N types of cars? Page 2 of 2