Simplex method for equality optimization

I have a linear model that goes as 0.1*x1 + 0.8*x2 + 3.4*x3 + 5.0*x4 + c and this linear model was generated by using a Linear Regression.

• MAE is ~ 0.4
• MSE is ~ 0.6
• R$$^{2}$$ score is 85.

The goal I want to achieve here is to optimize this function i.e. to find the right values for x1, x2, x3 and x4, by given constraints such as 30 < x1 < 45, 55 < x2 < 60, etc., so the final number of the model would be 150 or 0.1*x1 + 0.8*x2 + 3.4*x3 + 5.0*x4 + c = 150.

I did a small research and it seems that one of the algorithms that does this kind of a linear optimization is Simplex.

However, I'm a total beginner when it comes to this and the research I did showed me only methods for either minimization or maximization. What is the right term for this kind of a problem? If anyone knows a similar example as in my case, could you share it? Also, if someone has solved a problems like this in the past, would you be kind to suggest other methods for optimizing my linear problem that work well?