Instructions: Prepare handwritten solutions to Problem la. Scan your handwritten work for Problem 1a into a single pdf and submit through Gradescope. Problem 1b involves building and solving an AMPL model. Submit your work on this problem as follows: Prepare a single submission to the Blackboard assignment "Lesson 12 Assignment - AMPL Submission"; After completing Problem 1b, attach to this submission (1) your model file and (2) a separate text file that contains the output of your AMPL session. Problem 1: Reconsider the snow shovel production/inventory model from class (i.e., Lesson 11 Example 1). This time, however, suppose you may produce at most 65,000 in any quarter but you must pay a fixed cost of $30,000 for every quarter in which you produce shovels. Full Problem Description: You are in the business of producing and selling snow shovels, and you need to determine how many shovels should be produced during each of the next four quarters to meet the following demands: 11,000 shovels in quarter 1; 48,000 shovels in quarter 2; 64,000 shovels in quarter 3; and 15,000 shovels in quarter 4. Due to labor limitations, at most 65,000 shovels can be produced in any one quarter at a cost of $5/shovel. Additionally, a fixed cost of $30,000 must be paid for any quarter in which shovels are produced. You may assume that any shovels produced during a quarter can be used to satisfy demand for that quarter. At the end of the quarter, a holding cost of $0.50 per shovel in inventory is incurred. Currently, you have no shovels in inventory. Part a: Formulate an integer-linear program to determine a production schedule that minimizes the sum of production and inventory costs over the next four quarters. (Begin your handwritten solution on a new page labeled "Problem 1" at the top.) Part b: Solve Problem 1 using AMPL/CPLEX and report the obtained optimal solution. (Save the model file as "lastname_firstname_112a_probl" and copy your AMPL session and output into a text file named "lastname_firstname_112a_probl_output." Attach these files to your Blackboard assignment submission.) Instructions: Prepare handwritten solutions to Problem la. Scan your handwritten work for Problem 1a into a single pdf and submit through Gradescope. Problem 1b involves building and solving an AMPL model. Submit your work on this problem as follows: Prepare a single submission to the Blackboard assignment "Lesson 12 Assignment - AMPL Submission"; After completing Problem 1b, attach to this submission (1) your model file and (2) a separate text file that contains the output of your AMPL session. Problem 1: Reconsider the snow shovel production/inventory model from class (i.e., Lesson 11 Example 1). This time, however, suppose you may produce at most 65,000 in any quarter but you must pay a fixed cost of $30,000 for every quarter in which you produce shovels. Full Problem Description: You are in the business of producing and selling snow shovels, and you need to determine how many shovels should be produced during each of the next four quarters to meet the following demands: 11,000 shovels in quarter 1; 48,000 shovels in quarter 2; 64,000 shovels in quarter 3; and 15,000 shovels in quarter 4. Due to labor limitations, at most 65,000 shovels can be produced in any one quarter at a cost of $5/shovel. Additionally, a fixed cost of $30,000 must be paid for any quarter in which shovels are produced. You may assume that any shovels produced during a quarter can be used to satisfy demand for that quarter. At the end of the quarter, a holding cost of $0.50 per shovel in inventory is incurred. Currently, you have no shovels in inventory. Part a: Formulate an integer-linear program to determine a production schedule that minimizes the sum of production and inventory costs over the next four quarters. (Begin your handwritten solution on a new page labeled "Problem 1" at the top.) Part b: Solve Problem 1 using AMPL/CPLEX and report the obtained optimal solution. (Save the model file as "lastname_firstname_112a_probl" and copy your AMPL session and output into a text file named "lastname_firstname_112a_probl_output." Attach these files to your Blackboard assignment submission.)