1-Example (1): Leather Factory wants to produce two types of womens handbags. After a good study of the stages of the production of these bags turned out to be one bag production requires the following stages: 1 Cut and leather dye 2 sewing. 3 finishes. 4 testing and packaging. Director was also able to provide the information given in the following table for the time required hourly production of each type in each stage, and the production capacity available in the factory calculated hour Cut and leather sewing finishes testing and packaging Profit Casual bag 7/10 1/2 1 1/10 10 Excellent bag 1 5/6 2/3 1/4 9 Available energy 630 600 708 135 Define by drawing all of the restrictions that can not be controlled and the constraints that can be controlled and the mathematical model2- Factory tents produces two types of tents large type and small type requires the production of small tent one working hour cut cloth and three hours of Compilation. requires the production of big tent one working 2 hour cut cloth and 4 hours of Compilation. the maximum hours available per week in each of the department shear assembly 32 84 hours in a row as the distributor can not sell more than 12 large tents week If small profit tent SR 200 and won big tent 320 SR Define by drawing all of the restrictions that can not be controlled and the constraints that can be controlled and the mathematical model3-There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is $25. The revenue per unit is projected to be $45. a. Write an expression for total cost. b. Write an expression for total revenue. c. Write an expression for total profit. d. Find the break-even point. 4-A snack food manufacturer buys corn for tortilla chips from two cooperatives, one in Iowa and one in Illinois. The price per unit of the Iowa corn is $6.00 and the price per unit of the Illinois corn is $5.50. a. Define variables that would tell how many units to purchase from each source. b. Develop an objective function that would minimize the total cost. c. The manufacturer needs at least 12000 units of corn. The Iowa cooperative can supply up to 8000 units, and the Illinois cooperative can supply at least 6000 units. Develop constraints for these conditions.5-As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast operation, the prospective owners have projected:Monthly fixed cost (loan payment, taxes, insurance, maintenance) $6000 Variable cost per occupied room per night $ 20 Revenue per occupied room per night $ 75a. Write the expression for total cost per month. Assume 30 days per month. b. Write the expression for total revenue per month. c. If there are 12 guest rooms available, can they break even? What percentage of rooms would need to be occupied, on average, to break even?6- Find the break-even point using excel the same example of the break-even point . also if the company seal 10 house what the profit