Westlake Corporation is manufacturing company that makes small electric motors it sells for $$45$ per unit. The variable costs of production are $$30$ per motor, and annual fixed costs of production are $$500,000.$ No credit will be given unless you show all you work$).$

Required

a$.$ How many units of product must Westlake make and sells to break even?

b$.$ How many units of product must Westlake make and sell to earn a $$135,000$ per profit?

c$.$ The marketing manager believes that sales would increase dramatically if the price were reduced to $$37$ per unit. How many units of product must Stone make and sell to earn a $$135,000$ profit, if the sales price is set at $$41$ per unit?