ME 2352 Design Optimization Assignment ONE, due January 25th, 2024, 4:00 pm University of New Brunswick Department of Mechanical Engineering Winter 2024 1. Weenies and Buns is a food processing plant which manufactures hot dogs and hot dog buns. They grind their own flour for the hot dog buns at a maximum rate of 200 lb./week. Each hot dog bun requires 0.1 lb. of flour. They currently have a contract with Pigland Inc., which specifies that the delivery of 800 lbs. of pork product is delivered every Monday. Each hot dog requires lb. of pork product. All the other ingredients in the hot dogs and hot dog buns are in plentiful supply. Finally, the labor force at Weenies and Buns consists of 5 employees working full time (40 hours per week each). Each hot dog requires 3 minutes of labor, and each hot dog bun requires 2 minutes of labor. Each hot dog yields a profit of $0.20, and each bun yields a profit of $0.10. Weenies and Buns would like to know how many hot dogs and how many hot dog buns they should produce each week so as to achieve the highest possible profit. Clearly formulate the problem in Standard Form: a) State the design variables; b) State the objective function; c) State all the constraints; and d) Solve the problem graphically. 2. A company owns two sawmills and two forests, see figure below. The table below shows the capacity of each mill (logs per day) and the distances between forests and mills (km). Each forest can yield up to 250 logs/day for the duration of the project, and the cost to transport the logs is estimated at $0.35/km/log. At least 350 logs are needed each day. The goal is to minimize the total cost of transportation of logs each day. Mill Distance, km Forest 1 A 24 Forest 2 20.5 B 17.2 18.0 Mill capacity/day 360 logs 450 logs Rev. Jan. 18th, 2024 Page 1 of 2 ME 2352 Design Optimization Assignment ONE, due January 25th, 2024, 4:00 pm University of New Brunswick Department of Mechanical Engineering Winter 2024 Forest 1 Forest 2 X4 X2 X3 Mill B Mill A Clearly formulate the problem in Standard Form: a) State the design variables; b) State the objective function; c) State all the constraints. d) Assume the employees of Mill B go on strike (i.e., Mill B is not operational). Re-formulate the problem and explain your new problem model. Solve graphically. e) Solve part d) graphically. 3. Write your own MATLAB code to plot two-dimensional linear programming problems. All constraints need to be properly labeled, indicating the type of constraints (e.g. LE, L, GE, G). Also, the objective function gradient line needs to be plotted showing the direction of improvement. The input to your code should be: A vector c for the objective function A matrix Aeq and a vector beq for the equality constraints A matrix Ale and a vector ble for the equality constraints A matrix Age and a vector bge for the equality constraints Include a help section on each and every function that you create. *LE for 'lower or equal', L for lower', GE for greater or equal', and G for 'greater' a) Use your code to produce the graph from Question #2; and then b) Compare the results obtained by hand (i.e., in Question #2) with the optimal solution you obtained from using the graph produced by your code. Rev. Jan. 18th, 2024 Page 2 of 2