A manufacturer of fitness equipment is planning the introduction of two new products: a regular version with a manufacturer's suggested retail price of $239 per year, and a superior version with a suggested retail price of $339 per year. The cost of the company is $195 per regular version and $225 per superior version, plus additional fixed costs of $400, 000 per year. In the competitive market the number of sales will affect the sales price. It is estimated that for each type of product, the sales price drops by one cent for each additional unit sold. Furthermore, sales of the regular product will affect sales of the superior product and vice versa. It is estimated that the price for the regular product will be reduced by an additional 0.3 cents for each superior product sold, and the price for superior product will decrease for by 0.4 cents for each regular product sold. The company believes that when the number of units of each type produced is consistent with these assumptions all units will be sold. a. How many units of each type of products should be manufactured such the profit of the company is maximized? Please formulate a nonlinear programming model and solve using Excel Solver. b. Now assume the company has limited resources which restrict the number of units of each type produced per year such that the regular product is less than 5, 000 units; the superior product is less than 8, 000 units; and the total amount of products are less than 10, 000 units. How would your results from part a change?