Every gram of wheat provides $0.1$ gram of proteins and $0.25$ gram of carbohydrates. The corresponding values of rice are $0.05$ gram and $0.5$ gram respectively. The minimum daily requirements of proteins and carbohydrates for an average child are $50$ gram and $200$ gram respectively. Then in what quantities wheat and rice be mixed in daily diet to provide minimum daily requirement of proteins and carbohydrates at minimum cost?