Problem 1 (based on Exercise 4-27 from the textbook). Midville Manufacturing assembles heavy duty materials handling carts to meet demand of 500 units in the first quarter of each year, 300 in the second, 1000 in the third, and 1200 in the fourth. Elementary components, which consist of wheels, steering yokes, and carrying platforms, are assembled separately. Then, each steering yoke is equipped with 4 wheels to form the front-end subassembly. Finally, front-end subassemblies are combined with a carrying platform and 8 additional wheels at the rear to complete the cart. Using j=1: Steering jokes j = 2: Wheels j = 3: Platforms j =4: Front-end assemblies j = 5: Finished carts the following table shows the estimated value of each element (in dollars) and the factory hours required to assemble it. j=1 Element Value Time 120 0.06 j = 2 j = 3 40 75 0.07 0.04 j=4 j = 5 400 700 0.12 0.32 Components, subassemblies, and finished carts produced in any quarter may be used or shipped in the same quarter or held as inventory. The holding cost per unit of inventory is 5% of the value of each product. Midville seeks a plan that minimizes these holding costs while conforming to the factory production capacity, 1150 hours per quarter. (a) Formulate an LP model to choose a production plan for Midville Manufacturing (6) Solve your model in AMPL. What is the optimal solution? What is the optimal value? (c) Suppose that now the demand values are unknown. What is the range for the demand in each quarter such that the optimal solution remains unchanged? (d) Suppose that Midville Manufacturing realizes that the value of finished charts is incorrect. How much can we modify its value so that the optimal solution remains the same