A business manufactures a product with variable costs of $3.20 per unit. The product is sold for $6.40 per unit. The business has fixed costs of $4,500 and aims for a profit of $12,500. The sales level in units required to achieve the desired profit is units.

The profit function for two products is: Profit3x12+42x13x22+48x2+700, where x1 represents units of production of product 1, and x2 represents units of production of product 2. Producing one unit of product 1 requires 4 labor-hours, and producing one unit of product 2 requires 6 labor-hours. Currently, 24 labor-hours are available. The cost of labor-hours is already factored into the profit function, but it is possible to schedule overtime at a premium of 5 per hour. a. Formulate an optimization problem that can be used to find the optimal production quantity of products 1 and 2 and the optimal number of overtime hours to schedule. b. Solve the optimization model you formulated in part (a). How much should be produced and how many overtime hours should be scheduled?

Lotts Company produces and sells one product. The selling price is 10, and the unit variable cost is 6. Total fixed cost is 10,000. Required: 1. Prepare a CVP graph with Units Sold as the horizontal axis and Dollars as the vertical axis. Label the break-even point on the horizontal axis. 2. Prepare CVP graphs for each of the following independent scenarios: (a) Fixed cost increases by 5,000, (b) Unit variable cost increases to 7, (c) Unit selling price increases to 12, and (d) Fixed cost increases by 5,000 and unit variable cost is 7.

Faldo Company produces a single product. The projected income statement for the coming year, based on sales of 200,000 units, is as follows: Required: 1. Compute the unit contribution margin and the units that must be sold to break even. Suppose that 30,000 units are sold above the break-even point. What is the profit? 2. Compute the contribution margin ratio and the break-even point in dollars. Suppose that revenues are 200,000 greater than expected. What would the total profit be? 3. Compute the margin of safety in sales revenue. 4. Compute the operating leverage. Compute the new profit level if sales are 20 percent higher than expected. 5. How many units must be sold to earn a profit equal to 10 percent of sales? 6. Assume the income tax rate is 40 percent. How many units must be sold to earn an after-tax profit of 180,000?