PLEASE SOLVE WITHOUT USING A SOLVER

Problem 4. A company can produce 1 unit of product C using a combination of 1 unit of input A and 2 units of input B. The company is planning its production for the next 6 months. 1. The demand for product C in month t is dt for t = 1, 2, ..., 6. The company must meet its demand exactly, i.e., the amount of product C sold in month t is exactly dt (for t = 1, 2, ..., 6). 2. The per unit purchasing price for input A is pt in month t (for t = 1, 2, ..., 6). The per unit purchasing price for input B is qt in month t (for t = 1, 2, ..., 6). 3. The per unit cost of production of product C is rt in month t (for t = 1, 2, ..., 6). 4. Inventory situation: The company can carry inventory of the inputs (i.e. the company can purchase more input than required in a given month and store the inputs for use in a later month) and the product C it manufactures (i.e. the company can manufacture more than demand and store it for later use). The per unit cost of storing inventory from month t to month t + 1 of input A, input B and product C is at, bt, ct respectively (for t = 1, 2, ..., 5). Write a linear program to find an optimal production and inventory plan (that is a plan that minimizes the total cost of production and inventory) for the company. 2