Suppose a company manufactures three products: Product A, Product B and Product C. The company wants to maximize its profit while adhering to certain constraints. The profit per unit for Product A is $10, for Product B, it's $15, and for Product C it is $17. The company has limited resources for production and distribution, which are as follows: The company has X hours of labor available per week. It takes 2 hours to make one A, 3 hours to make one B, and 3.5 hours to make one C. (Each student has a different X value!) Available raw materials are only enough for 500 units of A, 600 units of B, and 450 units of Product C. The warehouse can store a maximum of 750 units of products, so the total number of products cannot exceed this limit. The weekly demand for Product A is 100 units. It is 150 units for Product B and 120 units for Product C. Production numbers for each product are integers, you cannot produce half a product. Based on the given constraints, create an integer programming problem to find the number of products to be produced weekly to maximize the company's weekly profit. Open a blank R Script file and do the following using the IpSolve package: 1. Define the objective function. 2. Define the constraints matrix. 3. Define the vector for the directions of the constraints. 4. Define the vector for the right-hand-side values of the constraints. 5. Define the integer vector. 6. Run the Ip() function to find the maximum profit (.objval), and the necessary production values to achieve the maximum profit (.solution). Grading rubric: Questions 1 to 5 0.7 pts each. Question 61.5 pts. X Values: Student ID X value A00650003 1200 A00627377 1230 A00630480 1260 A00636125 1290 A00632344 1320 Student ID X value A00646068 1350 A00649516 1380 A00662740 1410 A00644770 1440 A00644331 1470 Student ID A00653105 1500 A00404040 1530 A00642816 1560 A00632486 1590 A00636685 1600 X value