You are starting a small business to sell toys. The demand for toys are unlimitand far exceeds your production capacity. The selling price for one toy is $10 and you areprice takers in the toy market (i.e. your production will not affect the market price). Theannual production depends solely on labor working hours:?@@<?A C('D<&$E'@ = 6 × GWhere N denotes the annual labor working hours. Moreover, in the labor market, thelabor’s working hours depend directly on hourly wage you pay:G = −2500 + 1000 × HWhere w denotes the hourly wage. In the first year of your business, you have a budget of$25000 as labor cost. Your goal is to maximize your annual profit = revenue – labor cost.a. (6 points)How do you formulate the annual revenue function from selling toys interms of hourly wage w ?b. (6 points)How do you formulate the total labor cost function in terms of w?c. (8 points)Write down a non-linear program for this optimization problem

Toys-4-U manufactures a toy that it sells for $30 each. The variable cost per toy is $15 and the fixed costs for this product line are $96,000 per year. They estimate they can produce 10,240 toys per production period.a. What is the break-even point in units?Break-even point            toys per yearb. What is the break-even sales revenue?Break-even sales revenue           $ per yearc. What is the break-even volume as a percent of capacity? (Round your answer to 1 decimal place.)Break-even volume            %d. What would their net income be if they sold 9,200 toys?Net income           $ e. What level of output is required to have a net income of $24,000?Level of output            toys per year

Manico Company produces three products-X, Y, & Z-with the following characteristics: XYZSelling price per unit$21.00$17.00$16.00Variable cost per unit12.6012.756.40Contribution margin per unit$ 8.40$4.25$9.60 === ======= ====== ====Machine hours per unit536The company has only 2,000 machine hours available each month. If demand exceeds the company's capacity, in what sequence should orders be filled if the company wants to maximize its total contribution margin? Question 19Answera.Orders for Y first, X second, and Z thirdb.Orders for X first, Z second, and Y thirdc.Orders for Z first, X second, and Y thirdd.Orders for Z first and no orders for X or Y

A seller would be willing to sell a product ONLY if the price received is: A. equal to the cost of production B. less than the cost of production C. at least double the cost of production D. at least as great as the cost of production

The unit cost of a toy is $C when n pieces of the toy are produced, and C =k/square root of n When 100 pieces of the toy are produced, the unit cost is $50. (a) Express C in terms of n. (b) If the unit cost of the toy is $25, how many pieces of toys are produced? (c) If the unit cost of the toy decreases by 20%, by what percentage does the quantity of toys produced increase?

Pawsome Playthings are a business that makes dog toys. The business has provided the following information:Product Sales Price Variable Cost Sales mixSqueaky Plush Toys 15 10.50 15Tug Rope Toys 10 5.00 10Treat-Dispensing Toys 30 12.00 7Fixed costs are $6,700.How many items in total need to be sold to break even? Please answer in whole units