Discuss the below problem:
Q: A manufacturer of a particular product produces x_1 units in the first week and x_2 units in the second week. The number of units produced in the first week must be at least 200. And the number of products produced in the second week must be at least 600, including first week products, to be able to supply the regular customers. The initial inventory is zero and the manufacturer ceases to produce the product at the end of the second week. The product cost of a unit in dollars, is given by 4x^2_i where x_i is the number of units produced in week i (I = 1, 2). In addition to the production cost, there is an inventory cost of $10 per unit for each unit produced in the first week that is not sold by the end of the first week. Solve the optimization problem using graphical optimization.