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There is a limit of 40 hours usage per week for each machine.

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Solving the following problem in Excel using solver, ( you can skip the a. part of the assignment); b. (5p) A businessman is considering opening a small specialized trucking firm. To make the firm profitable, it is estimated that it must have a daily trucking capacity of at least 84,000 cu. ft. Two types of trucks are appropriate for the specialized operation. Their characteristics and costs are summarized in the table below. Note that truck 2 requires 3 drivers for long haul trips. There are 41 potential drivers available and there are facilities for at most 40 trucks. The businessman's objective is to minimize the total cost outlay for trucks. Capacity Drivers Truck Cost (Cu. ft.) Needed Small $18,000 2,400 1 Large $45,000 6,000 3 Solve the problem with excels solver and note there are alternate optimal solutions. i) Which optimal solution does excel’s solver give? Find with a slightly changed model, which optimal solution: ii) uses only one type of truck? iii) utilizes the minimum total number of trucks? iv) uses the same number of small and large trucks? c. (6p) Three products can be produced at two machining centers during a one-week period. The products may be produced in fractional amounts. The linear relationships describing this situation are listed below. The variables and constraints are: A, B and C are the amounts of the three products in units. The revenue per unit is $20, $30 and $25 respectively. R1 and R2 are the amounts of raw materials used in kilograms. The cost per kilogram is $6 and $8 respectively. Two machines perform operations on the product. Each machine is available for 40 hours during the week. The operation times are shown in the machine constraints. The market limits production in each week for A, B and C to 10, 20 and 10 units respectively. Based on this information a linear programming model is shown below. All the variables in the above model may assume fractional values. Max. Profit: P = 20A + 30B + 25C - 6R1 - 8R2 Subject to: Time limit on machine 1: 5A + 8B + 10C <= 40 (hours) Time limit on machine 2: 8A + 6B + 2C <= 40 (hours) Raw material 1 used: R1 = 1A + 2B + 0.75C Raw material 2 used: R2 = 0.5A + 1B + 0.5C Market Limits and non-negativity: 0 <= A <= 10, 0 <= B <= 20, 0 <= C 0, the charge is $50. ii. There is a limit of 40 hours usage per week for each machine. There is a setup time for each product that is 5 hours per setup on machine 1, and 3 hours per setup on machine 2. The setup times reduce the hours available to produce the products. The setup times are the same for each product. iii. In addition to the machines you already own, you are allowed to purchase up to two more machines of each type. Each machine provides a work capacity of 40 hours per week. To add one additional machine of type 1 the cost is $50 per week. To add a third machine of type 1, the cost is $45 per week. To add one additional machine of type 2 the cost is $75 per week. To add a third machine of type 2, the cost is $60 per week.

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