Car Manufacturing Industry: A Case Study

A car manufacturing company needs to find the proper combination of four materials, such that all four metals are present in the alloy, in proper proportion as per the standards prescribed by ARAI.

Consider the table given below that gives the chart of the materials, metals, and ARAI$-$prescribed standards:

MaterialMetal $1$Metal $2$Metal $3$Metal $4$Cost per $100$ g in Rs$.|$ Weight of$|$ #$1|12|2|4|2|20$metal in$|$ #$2|4|8|2|4|40$g per $100$ g of$|$ #$3|6|2|6|4|20$the material$|$ #$4|6|6|4|4|20|$ ICMR$|$ Stds$.$ in g$|$ At most $50|$ At most $30|$ At most $36|$ At least $24|$Let

$$

$$

x

i

$$

denote the number of slabs of material

$$

i of $100$g each. Note that slabs can be further dividied.

Please take note of the following:

According to the ARAI standards, the weight of metals $1,2,$ and $3$ should be at most $50,30,$ and $36$ g$,$ respectively, and the weight of metal $4$ should be at least $24$ g in the alloy.

Respond to Questions $4$ and $5$ based on Phase $2$ case.