A company produces two popular chemical-based products: a fuel additive and a solvent base. The demand for these two items is sensitive to price, and historical data indicate that the monthly demands are given by D_F = 1.5P_F 750 and D_S = 2.5P_S - 960 , where D_F = demand for the company's fuel additive in tonnes, D_S = demand for the company's solvent base in tonnes, P_F = price per tonne of its fuel additive, and P_S = price per tonne of its solvent base.

The cost to produce a tonne of its fuel additive is $120, and the cost to produce a tonne of its solvent base is $140. To remain competitive, the company must price its fuel additive and solvent base at no more than $270 and $300 per tonne, respectively.

Formulate the algebraic model for this problem by writing down the decision variables, objective function, and constraints, to maximise total profit from both the fuel additive and solvent base.