IED Inc. operates two manufacturing plants $($ A and $B)$ that have the capability to produce three different

products for the aerospace industry: Ailerons, Elevons, and Flaps. Your consulting group "Optimize

Consulting" is responsible to determine a production, inventory, distribution, and marketing plan for the

next six periods that will ensure profit maximization and provide management with a useful decision$-$

making tool.

In order to facilitate your analysis, IED Inc, has gathered the necessary system requirements that will be

needed for your model. These include the revenues generated from sales, costs incurred throughout the

manufacturing process, as well as projected demand for all periods:

Revenues are generated by selling ailerons, elevons, and flaps at the following unit prices:

Costs associated with obtaining raw materials, production, storage and shipping are summarized below.

Plant A has $1800$ hours of regular time labor available per period and plant B has $2800$ hours of regular

time labor available per period. Overtime hours can be scheduled at both plants if necessary. Your group

needs to incorporate special restrictions into the model to ensure that labor in consecutive periods does

not differ by more than five pereent. The table below shows costs associated with regular and overtime

labor for each period.

Two types of raw materials are used: $1$ and $2.$ There are $140,000lbs.$ of raw material $1$ and $4,000lbs.$ of

raw material $2$ available each period. Costs differ between plants because of the proximity of the vendor

in relation to each plant. Raw material costs for each plant are:

Once an aileron, elevon, or flap is produced, it is either sent to the distribution center $($DC$)$ or stored until

the next period. There is a limit on the number of products $($units$)$ that can be kept in storage at the end of

any given period because of the size of the storage area in each plant. A maximum of $40$ units of all

products combined can be stored in plant A and $60$ units can be stored in plant B$.$ Shipping and inventory

costs are shown below.

The sales department provided the following production requirements based on customer contracts and

agreements that must be met throughout the next six periods of production.

Supplemental demand can be created by advertising. Advertising in any given period has an effect on

demand in future periods. The unit investment costs below reflect the cost to generate one unit of

additional demand in that period plus the demand generated in future periods. IED Inc. had allocated an

advertising budget of $$100,000$ for all six periods.

Each unit produced has the following requirements based on the type of product $($ailerons$,$ elevons, or

flaps$)$ and the plant at which it is produced. These requirements are summarized below. solve it using linear programming and explain every constraints.