Week 6/7 : Exercise 1. Consider the following integer programming case: maximize Z = 6P+4Q subject to 3P + 4Q ≤10 P, Q ≥0 and integer The max Z is: A. 15 B. 21 C. 8 D. 18 2. In an Integer programming model, can constraints have decimals like: 5A+0.6B<=8.2 A. No B. Yes 3. The owner of a machine shop is planning linear to expand by purchasing some new machines. The number of machines the owner can purchase is limited by the cost of machine. The owner can invest $1,000,000 max. If M1 is the number of machine 1 and M2 is the number of machine 2, purchase price of M1 is $45,000 and M2 is $88,000 then the constraints are: A. B, & C are both wrong B. 45M1+88M2 ≤1000 C. 45M1+88M2 ≤1000 and M1,M2 ≥0 and integer 4. Auto shop capacity: Shop Capacity Standard Fancy Luxury Engine 120 3 2 1 A Body 80 1 2 3 B Standard Finishing 96 2 C Fancy Finishing 102 3 D Luxury Finishing 40 2 E Contribution $840 $1120 $1200 Also it is not possible to produce negative number of cars of any type F In this problem there are six constraints – A, B, C, D, E, F A. What product mix maximizes the profit? B. How much extra profit is possible if the plant is allowed to produce negative number of cars of any specific type? C. If investing in infrastructure is not an issue what must be done to increase the maximum profit by 15.56%? (HINT: new max profit – old max profit/old max profit = 0.1556) D. What will be your suggestion to increase the maximum profit by $20640? (NOTE: max profit not just profit). E. In our original problem as stated above, there are some constraints that have no real effect, which are they? F. In our original problem, what product mix will generate exactly $50,000 in profit? G. Choose the right answer: Look at the first constraint A. It means: A. Engines for 3 standard cars, 2 fancy cars, and 1 luxury car can be manufactured in no greater than 120 hours in the engine shop B. It takes 3 hours to manufacture the engine for a standard car, 2 hours for a fancy car, and 1 hour for a luxury car and in total we have no greater than 120 hours in the engine shop C. The solver has to make sure the ratio of cars manufactured is always 3:2:1 for standard, fancy, and luxury D. None of the above is true
