Develop a linear optimization model to determine the optimal mix to maximize profit. Define variable names to use for the number of units of each product shipped to each distribution center.

Linear Optimization

Mirza Manufacturing makes four electronic products, each of which comprises three main materials: magnet, wire, and casing. The products are shipped to three distribution centers in North America, Europe, and Asia. Marketing has specified that no location should receive more than the maximum demand and that each location should receive at least the minimum demand. The material costs per unit are magnet–$0.61 , wire–$0.31 , and casing–$0.33 . The following tables show all of the production information, including the number of units of each material required in each unit. Develop and solve an appropriate linear optimization model to maximize net profit.

First, develop a linear optimization model to determine the optimal mix to maximize profit. Define variable names to use for the number of units of each product shipped to each distribution center. For the purposes of this solution process, use NAA for units of product A shipped to the North American distribution center, NAB for units of product B shipped to the North American distribution center, EUA for units of product A shipped to the European distribution center, AA for units of product A shipped to the Asian distribution center, and so on.

Next, identify the objective function. In this case, the objective function is the total profit, the total revenue minus all of the costs. Write the objective function.
Profit Total Revenue Total Production Cost Packing and Shipping Costs Material Cost= − − −
Next, write an equation to calculate each term in the objective function. Write the equation for total revenue.Write the equation for total production cost.
Write the equation for packaging and shipping costs.
Write the equation for the material cost. To do so, first find the equations for the total number of materials used. Start with total number of magnets used.
Next, write the equation for the amount of wire used.
Next, write the equation for the amount of casing used.
Write the equation for the material cost.
Material Cost (Magnets used) (Wire used) (Casing used)= 0.61 + 0.31 + 0.33
Next, write each constraint as a mathematical equation or inequality. In this case, the minimum and maximum demand and the available raw material.
Write the constraint for the demand for Product A in North America.
Write the constraint for the demand for Product B in North America.
Write the constraint for the demand for Product A in Europe.
Write the constraint for the demand for Product A in Asia.