Mathematical modeling

espectively. If 100 units of raw materials and 120 units of time are available,formulate a linear programming model for this problem to determine how manyunits of each type of concrete elements should be produced to maximize profit.4. A contractor may purchase material from two different sand and gravel pits. Theunit cost of material including delivery from pits 1 and 2 is LE 50 and LE 70 percubic meter, respectively, the contractor requires at least 100 cubic meter of mix.The mix must contain a minimum of 30% sand. Pit 1 contains 25% and pit 2contains 50% sand. If the objective is to minimize the cost of material, define thedecision variables and formulate a mathematical model.- Draw the feasible region- Determine the optimum solution by the graphical method- Label the active and inactive constraints- Use Solver to model and solve this problem5. As the director of waste management, you are trying to plan next year’soperations for the disposal of solid waste. You have three options for disposal:OptionLocal county-owned landfillIncinerationContract landfillDisposal cost (LE/ton)6109There are 300,000 people living in the county with an average of 2.75 kg percapita per day of solid waste. Several constraints are applied to the problem:- The total budget for solid waste disposal is LE 3,000,000.- At least LE 300,000 in disposal income is needed to maintain the local landfill.- At least LE 75,000 in disposal income is needed to maintain the incinerator.- The capacity of the incinerator is 50 ton/day (assume 250 working days).- You don’t want to place in excess of 50% of the waste in the local landfill.Formulate a linear program model to produce an optimal plan for solid wastemanagement.Systems Analysis 45 Dr. Emad Elbeltagi