Write the mathematical model for constraint

Techomaxo helps the rail industry to achieve decreased costs and downtime to have more reliable, comfortable journeys for their passengers. Techomaxx does this by helping rail companies, operators, and suppliers to improve their designs considering durability, efficiency, and noise/vibration issues. In the following table, the demand in thousands for the three products is shown. Techomaxx currently has one factory in Nottingham, the UK that produced all three products for the entire country. The gear line in the Nottingham facility had a capacity of 35 million units, an annualized fixed cost of $35 million a year, and a variable cost of $200 per unit. The axle box bearing line in the Nottingham facility had a capacity of 3 million units, an annualized fixed cost of $4.5 million a year, and a variable cost of $400 per unit. The optimized simulation software line in the Nottingham facility had a capacity of 3.5 million units, an annualized fixed cost of $8.5 million a year, and a variable cost of $540 per unit. The current transportation costs per unit are given in the following table. The manager had identified Cardiff, Sheffield, and Exeter as potntial sites for new plants. Each new plant could have a gear line, an axle box bearing line, an optimized simulation software line, or all. A new Gear line had a capacity of 55 million units, an annual fixed cost of $6.5 million, and a variable production cost of \$180 per unit. An axle box bearing line had a capacity of 5 million units, an annual fixed cost of $6.5 million a year, and a variable cost of $320 per unit. A new optimized simulation software line had a capacity of 5.5 million units, an annual fixed cost of $10.5 million, and a variable production cost of $450 per unit. Develop a model for the manager to decide whether to build a new plant or not. Let Xijk and Yik be the decision variables of the model. Xjk: the amount of product k sent from factory i to region j. Yik={1, If product k is produced in factory 1;0, otherwise. a) (5 points) Satisfy the demand at each region. b) ( 5 points) Specify the capacity constraints. c) (5 points) Define the constraints under the situation of the Cardiff facility is open. d) (5 points) Assign the nonnegativity and binary variables constraints