please post all formulas and excell sheet if applicable.

A mower manufacturer produces 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 lawn service companies. The company is interested in establishing a pricing policy for the two mowers that will maximize the 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. 91 - 950 - 1.5p. +0.7p2 42 = 2500+ 0.3p. -0,5p Where 91 = number of residential mowers sold 92 = number of industrial mowers sold pi= selling price of the residential mower in dollars p2 = 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 $1,500 per mower. The fixed cost of production for the industrial mower is $30,000 and the variable cost is $4,000 per mower a) The company traditionally priced the lawn mowers at $2,000 and $6,000 for the residential and industrial mowers, respectively. Calculate the number of mowers that will be sold, and the profit with this pricing policy? b) Formulate a mathematical model to solve this problem optimally. Clearly define your decision variables, constraints and objective function c) Implement the model you formulated in (b) using Excel and find the optimal prices, profit and number of units sold using Excel Solver. Include a snapshot of your solution in the report. Compare the optimal answer you obtained to that in (a)