$(20)$A COMPANY HAS THREE PRODUCTION PLANTS AND THREE DISTRIBUTION SITES NUMBERS IN THE MATRIX SHOW TRANSPORTATION COST PER TON OF PRODUCT PER UNIT COST OF PRODUCTION AT PLANT $1,2,3$ ARE $2,3,4$ DOLLARS RESPECTIVELY.THE COMPANY WANTS TO MAXIMIZE ITS PROFITS

FORMULATE PROBLEM AS A LINEAR PROGRAMMING PROBLEM SET UP THE PROBLEM ONLY THE PRICE OF THE PRODUCT IS $20$ USD, $24$ USD, AND $20$ USD AT SITES A$,$ B$,$ AND C RESPECTIVELY.

$\backslash$table$[[,,$SITE A$,$SITE B$,$SITEC,CAPACITY$($TON$)],[$PLANT I,$20,10,4,$II$,70],[$PLANT $2,$U$,12,5,8,50],[$PLANT $3,,9,7,6,160],[$DEMAND$($TON$),,100,100,70,]]$