A fertilizer company blends silicon and nitrogen to produce two types of fertilizers. Fertilizer $1$ must be at least $40\%$ nitrogen and sells for $$70$ per pound. Fertilizer $2$ must be at least $70\%$ silicon and sells for $$40$ per poundThe company can purchase up to $8000$ pounds of nitrogen at $$15$ per pound and up to $10,000$ pounds of silicon at $$10$ per poundAssuming that all fertilizer produced can be sold, determine how the company can maximize its profit. $[$Hint: Total profit$-$selling price$-$ purchasing price$]$