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A plant that manufactures a variety of specialized steel

assemblies for the heavy construction equipment

industry is considering introducing $4$ new assemblies

to the market. The material specifications, amount of

resources available and potential profit per unit are

provided in the table below. Because of production

constraints, the company must use at least $900,800kg$

of Steel Plate in its production mix. In addition, for

each unit of Assembly Type $2$ it produces, it must

produce $2\mathrm{.}5($times$)$ of Assembly Type $1.$ At least $300$

Assembly Type$1$ units must be produced. Assuming

the company can sell all products it makes, develop a

linear programming $($LP$)$ model that can be solved

to obtain the optimal manufacturing strategy, to

maximize profit.

Let the number of units of Type $1,$ Type $2,$ Type $3,$ and Type $4,$ assemblies be: $x1,x2,x3,$ and X$4,$ respectively.