A poultry producer's stock requires at least $124$ units of nutritional element A and $60$ units of nutritional element B daily. Two feeds are available for use. One pound of Feed $1$ costs $16$ cents and contains $10$ units of A and $3$ units of B$.$ One pound of Feed $2$ costs $14$ cents and contains $4$ units of A and $5$ units of B$.$ Formulate the problem as UP and use graphical method to determine for the producer the least expensive adequate diet by combining the two feeds.