Formulate ONLY $($Do Not Solve$)$ the Linear Program for the following:

You are trying to create a budget to optimize the use of a portion of your disposable income.$$ You have a maximum of $$1500$ per month to be allocated to food, shelter, and entertainment.$$ The amount spent monthly on food and shelter combined must not exceed $$1000.$ The amount spent monthly on shelter alone must not exceed $$700.$ Entertainment cannot exceed $$300$ per month.$$ Each dollar spent on food has a satisfaction value of $2$; each dollar spent on shelter has a satisfaction value of $3$; each dollar spent on entertainment has a satisfaction value of $5.$ Assume a linear relationship, determine the optimal allocation of funds to maximize your satisfaction.$$ Formulate the linear program $($i$..$e$.$ the system of equations$)$ to model this problem.