Lydell Corporation currently operates in two states, P and Q$.$ State P has a $5$ percent tax rate and uses an equally weighted three$-$factor apportionment formula. State Q has a $9$ percent tax rate and uses an apportionment formula that double$-$weights the sales factor. For the current year, Lydell$$s state taxable income before apportionment was $$1,500,000.$ Following is information regarding Lydell$$s current activity within each state

State P State Q Total

Sales $$3,000,000$ $$2,000,000$ $$5,000,000$

Payroll $$1,000,000$ $$500,000$ $$1,500,000$

Average property $$1,200,000$ $$800,000$ $$2,000,000$

Lydell is considering expanding its operations by constructing a new production facility. The facility would increase Lydell$$s total property and payroll by $$1$ million and $$400,000,$ respectively. The company projects that, as a result of the new facility, total sales would increase by $$800,000,$ of which half of these new sales would be to customers in State P and half would be to customers in State Q$.$ Total net income would increase by $$300,000.$ Solely on the basis of state income tax considerations, in which state would you recommend Lydell locate the new facility?