The RMC corporation blends $3$ raw materials to produce two products: a fuel additive and a solvent

base. Each ton of fuel additive is a mixture of $2/5$th ton of material $1,3/5$th ton of material $3.$ A ton of

solvent base is a mixture of $(1)/(2)$ ton of material $1,1/5$th ton of material $2,$ and $3/10$th ton of material $3.$

RMC$$s production is constrained by a limited availability of the three materials. For the current

production period, RMC has the following quantities of each raw material: $20$ tons of material $1$; $5$ tons

of material $2$; $21$ tons of material $3.$ Management wants to achieve the following goals $($no priority$)$:

Goal $1$: Produce at least $30$ tons of fuel additive

Goal $2$: Produce at least $15$ tons of solvent base

The mathematical formulation of the above problem is as follows: