Linear Inequalities

Vitamins $\mathrm{A}$ and $\mathrm{B}$ are found in food ${\mathrm{F}}_1$ and ${\mathrm{F}}_2.$ One unit of ${\mathit{F}}_1$ contains 20 units of vitamin $\mathrm{A}$ and 30 units of vitamin B. One unit of food ${\mathrm{F}}_2$, contains 60 units of $\mathrm{A}$ and 40 units of B. Costs per unit of $\mathit{F}$, and ${\mathit{F}}_2$ are $\mathrm{₹}3$ and $\mathrm{₹}4$ respectively. The minimum daily requirement of vitamin $\mathrm{A}$ and $\mathrm{B}$ is 80 and 100 units respectively. Problem is to determine the mixture of food ${\mathrm{F}}_1$ and ${\mathrm{F}}_2,$ which meets the requirement at minimum cost by assuming that ${\mathit{x}}_1$ units of food ${\mathrm{F}}_1$ and ${\mathrm{X}}_2$ units of food ${\mathrm{F}}_2$ are required to fulfill the need of vitamins. The constraints are