The manager of a small firm is considering whether to produce a new product that would require leasing some special equipment at a cost of $20,000 per month. In addition to this leasing cost, a production cost of $10 would be incurred for each unit of the product produced. Each unit sold would generate $20 in revenue. Develop a mathematical expression for the monthly profit that would be generated by this product in terms of the number of units produced and sold per month. Then determine how large this number needs to be each month to make it profitable to produce the product. 1.2. Refer to Problem 1.1. A sales forecast has been obtained that indicates that 4,000 units of the new product could be sold. This forecast is considered to be quite reliable, but there is considerable uncertainty about the accuracy of the estimates given for the leasing cost, the marginal production cost, and the unit revenue. Use the Break-Even Analysis module in the Interactive Management Science Modules to perform what-if analysis on these estimates. a. How large can the leasing cost be before this new product ceases to be profitable? b. How large can the marginal production cost be before this new product ceases to be profitable? c. How small can the unit revenue be before this new product ceases to be profitable