Management for company objectives with considerations of optimal production/sales planning

Total profit level increases if a company increases the cost for achieving R&D related goals of equipment productivity enhancement, production cost saving, or for achieving equipment scale target, sales volume goal. But how much money should be invested to achieve a certain level of profit? We formulated the model to set the optimal goal levels to minimize the investment cost under the constraint that certain level of total profit should be guaranteed. This model derived from a case of P steel company. We found that this should be considered in relation with the production sales planning (known as optimal product mix problem) to guarantee the profit. We suggested a nonlinear programming model, a variant form of the product mix problem. We can find the optimal investment level for the R&D related goals or sales volume goal, equipment scale target for the P steel company using the model.