1.[25 points] Lawn King manufactures two types of riding lawn mowers. One is a low-cost mower sold primarily to residential home owners; the other is an industrial model sold to landscaping and lawn service companies. The company is interested in establishing a pricing policy for the two mowers that will maximize the gross profit for the product line. A study of the relationships between sales prices and quantities sold of the two mowers has validated the following price-quantity relationships. where 91-950-1.5p +0.7p 92 = 2500+ 0.3p1 - 0.5p2 91 q = number of residential mowers sold q = number of industrial mowers sold P = selling price of the residential mower in dollars p = selling price of the industrial mower in dollars The accounting department developed cost information on the fixed and variable cost of producing the two mowers. The fixed cost of production for the residential mower is $10,000 and the variable cost is $1500 per mower. The fixed cost of production for the industrial mower is $30,000 and the variable cost is $4000 per mower. Management's objective is to determine the selling price of residential mover and industrial mower that will maximize the total profit. Show your mathematic formulation of this problem, and solve this problem in Excel.