document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127117>Question 1127117</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a chocolate manufacturing company produces only two types of chocolate, A and B. On each sale, the company makes a profit of $6 per unit of A sold and $5 per unit of B sold. Both the chocolates require milk and chocolate only. Each unit of A requires 1 unit of milk and 3 units of chocolate. Each unit of B requires 1 unit of milk and 2 units of chocolate. The company kitchen has a total of 5 units of milk and 12 units of chocolate. The company wishes to maximize its profit. How many units of A and B should it produce respectively? Let the total number of units produced of A equal x and the total number of units of B produced by y. Note: Number of units can only be positive. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743518 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=743518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The constraint inequalities are...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By+%3C=+5 ALIGN=MIDDLE  ALT=\"x%2By+%3C=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  1 unit of milk for each of A and B; 5 units available<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2y+%3C=+12 ALIGN=MIDDLE  ALT=\"3x%2B2y+%3C=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  3 units of chocolate for A, 2 units for B; 12 units available<br><BR>\n" );
document.write( "Graph the constraint equations and find the point of intersection to determine the feasibility region.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C6%2C-2%2C6%2C5-x%2C6-1.5x%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-2%2C6%2C-2%2C6%2C5-x%2C6-1.5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The intersection point (algebraically, or from the graph) is (2,3).<br><BR>\n" );
document.write( "The objective function for the problem is the total profit, which is $6 per unit for A and $5 per unit for B:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B5y ALIGN=MIDDLE  ALT=\"6x%2B5y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Evaluate the objective function at each corner of the feasibility region: (0,0), (0,5), (2,3), and (4,0).<br><BR>\n" );
document.write( "(0,0): 6x+5y = 0<BR>\n" );
document.write( "(0,5): 6x+5y = 25<BR>\n" );
document.write( "(2,3): 6x+5y = 12+15 = 27<BR>\n" );
document.write( "(4,0): 6x+5y = 24<br><BR>\n" );
document.write( "The maximum profit is when they make 2 units of A and 3 units of B. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );