Please make an algebraic model for this question and solve on lingo or excel solver. thanks

A company which produces a single product has definite orders for this product over the next six months as follows: The company ended the previous month (month 0 ) with an inventory of 200 units, and the previous month production level was 400 units. The company wishes to end this six-month planning period with an inventory of at least 50 units. It costs $3.50 per unit to increase the production level from one month to the next, and $6.00 per unit to decrease it. The cost of holding inventory from one month to the next is $4.80 per unit per month. No shortages are permitted. In each month, the company wants to produce an integer number of units. The company wishes to minimize the sum of production level change costs and inventory costs over the six-month planning horizon. (a) Formulate an algebraic model for the problem. If you wish to solve the models in Excel Solver, you will have to write them in standard form, i.e. all variables on the left-hand side, and a number of the right-hand side. If you use LINGO, you are not bound by this restriction. Submit the algebraic model in the single Word or pdf file. (b) Use LINGO or the Excel Solver to solve this model. Imbed the LINGO model and solution report files, or tabs of the model and Answer Report from the Excel file, into the single Word or pdf submission file