1 Finco has the following investments available: Investment A o Investment B o For each dollar invested at time 0, we receive $0.10 at time 1 and $1.30 at time 2. (Time 0 = now; time 1 = one year from now; and so on.) For each dollar invested at time 1, we receive $1.60 at time 2. Investment C o For each dollar invested at time 2, we receive $1.20 at time 3. At any time, leftover cash may be invested in T-bills, which pay 10% per year. At time 0, we have $100. At most, $50 can be invested in each of investments A, B, and C. Formulate an LP that can be used to maximize Finco's cash on hand at time 3. Test your solution assigning certain amount of cash to your model and state conclusions. Problem 2 All steel manufactured by Steelco must meet the following requirements: 3.2-3.5% carbon; 1.8-2.5% silicon; 0.9-1.2% nickel; tensile strength of at least 45,000 pounds per square inch (psi). Steelco manufactures steel by combining two alloys. The cost and properties of each alloy are given in the following table: Alloy 1 Alloy 2 Cost per ton ($) $190 $200 Percent silicon 2 2.5 Percent nickel 1 1.5 Percent carbon 3 4 Tensile strength (psi) 42,000 50,000 Assume that the tensile strength of a mixture of the two alloys can be determined by averaging that of the alloys that are mixed together. For example, a one-ton mixture that is 40% alloy 1 and 60% alloy 2 has a tensile strength of 0.4(42,000) + 0.6(50,000). Use linear programming to determine how to minimize the cost of producing a ton of steel. Test the solution of your model with adequate values and draw conclusions. Problem 3 Steelco manufactures two types of steel at three different steel mills. During a given month, each steel mill has 200 hours of blast furnace time available. Because of differences in the furnaces at each mill, the time and cost to produce a ton of steel differs for each mill. The time and cost for each mill are shown in the following table: Steel 1 Steel 2 Mill Cost Time (Minutes) Cost Time (Minutes) 1 $10 20 $11 22 2 $12 24 $9 18 3 $14 28 $10 30 Each month, Steelco must manufacture at least 500 tons of steel 1 and 600 tons of steel 2. Formulate an LP to minimize the cost of manufacturing the desired steel. Test the solution of your model with adequate values and make conclusions Problem 4 The production-line employees at Grummins Engine work four days a week, 10 hours a day. Each day of the week, (at least) the following numbers of line employees are needed: Monday-Friday, 7 employees; Saturday and Sunday, 3 employees. Grummins has 11 production-line employees. Formulate an LP that can be used to maximize the number of consecutive days off received by the employees. For example, a worker who gets Sunday, Monday, and Wednesday off receives two consecutive days off. Test the solution of your model with adequate values and draw conclusions