a$.$ Without resorting to calculations, what is the total contribution margin at the break$-$even point? Explain why you chose the number for full marks.b$.$ Management is contemplating the use of plastic gearing rather than metal gearing in Product SW$.$ This change would reduce variable costs by $$15.$ The company's marketing manager predicts that this would reduce the overall quality of the product and thus would result in a decline in sales to a level of $350$ units per month. Should this change be made?c$.$ Assume that Challenger Company is currently selling $400$ units of Product SW per month. Management wants to increase sales and feels this can be done by cutting the selling price by $$25$ per unit and increasing the advertising budget by $$20,000$ per month. Management believes that these actions will increase unit sales by $50\%.$ Should these changes be made?d$.$ Assume that Challenger Company is currently selling $400$ units of Product SW$.$ Management wants to automate a portion of the production process for Product SW$.$ The new equipment would reduce direct labour costs by $$20$ per unit but would result in a monthly rental cost for the new robotic equipment of $$10,000.$ Management believes that the new equipment will increase the reliability of Product SW thus resulting in an increase in monthly sales of $12\%.$ Should these changes be made?$$