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# ENGG7302 Advanced Computational Techniques In Engineering

## Question:

[20 points] Mr. Optimal wants to find the values of x ∈ [0, 2π] that minimize the functions f(x) = sin(x), g(x) = 5 sin(x), and h(x) = sin(5x) using Generalized Pattern Search. Please sort the functions (i.e., f, g, and h) based on the difficulty of finding the desired value using Generalized Pattern Search, and as usual, please explain your answer. 2. [10 points] Is the following problem LP? max x · cos(a) + y · cos(b) for a particular a, b ∈ [0, 2π] subject to 2x + 5y ≤ 10 x ≥ 0 ; y ≥ 0 3. [20 points] Congratulations, you’ve been appointed to be the new Finance Director of UQ Humongous Data Training Consulting (UQ-HDTC)! You have three lines of training modules: Company Training (CT), On-line Training (OT), and Academic Training (AT).

For each sold CT, UQ-HDTC will receive \$1,000 in revenue, while for each sold OT, UQ-HDTC will receive \$800 and for each AT, it will receive \$700. Each module lasts for one month. To deliver the module CT, UQ-HDTC requires 100 hours of data scientist and computer programmer time. The module OT requires 300 hours of data scientist and 500 hours of computer programmer time, while AT requires 200 hours of data scientist and 100 hours of computer programmer time. Suppose UQ-HDTC has purchased 1,000 hours of data scientists time and 800 hours worth of computer programmer time for each month.

How many CT, OT, and AT modules you should sell per month, so as to maximize UQ-HDTC revenue, given the constraints on data scientist and computer programmer time? Please form the problem as an LP problem and solve it using Tableu form of Simplex method. 4. [20 points] You have 5 \$2 coins, 6 \$1 coins, 8 \$0.5, and no other money. You have to pay a given amount C, where no change is given. Of course, you want to minimize overpay. Please formulate this problem as a constrained optimization problem. Is this problem linear? 1 5. [30 points] A paper recycling machine can produce toilet paper, writing pads, and paper towels, which sell for 18, 29 and 25 cents and consume 0.5, 0.22 and 0.75 kilograms of newspaper and 0.2, 0.4, and 0.22 minutes.

Each day 10 hours and 1500 kilograms of newspaper are available, and at least 1000 rolls of toilet paper, 200 writing pads and 400 rolls of paper towels are required. (a) [10 points] Please formulate an appropriate LP to maximize revenue and solve it using tableau form of simplex method. (b) [20 points] Suppose a company asked to buy your newspapers, instead. What should be the minimum price this?

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