document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188280>Question 1188280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mrs. Diez has savings account in two banks. The combined amount of these saving is at least 150,000. <BR>\n" );
document.write( "One bank gave an interest of 4% while the other bank gives 6%. <BR>\n" );
document.write( "In a year, Mrs. Diez receives at most 12,000.<BR>\n" );
document.write( "1. What mathematical statements represent the given situation?<BR>\n" );
document.write( "2. Draw the graphs of the mathematical statments.<BR>\n" );
document.write( "3. How will you detemine the amount of savings in each bank account?<BR>\n" );
document.write( "4. Give one possible amount of savings in both accounts. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819900 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=819900\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Mrs. Diez has savings account in two banks. The combined amount of these saving is at least 150,000.<BR>\n" );
document.write( "One bank gave an interest of 4% while the other bank gives 6%.<BR>\n" );
document.write( "In a year, Mrs. Diez receives at most 12,000.<BR>\n" );
document.write( "1. What mathematical statements represent the given situation?<BR>\n" );
document.write( "x = amount invested at 4%.<BR>\n" );
document.write( "y = amount invesed at 6%.<BR>\n" );
document.write( "x + y >= 150000<BR>\n" );
document.write( ".04x + .06y <= 12000<BR>\n" );
document.write( "2. Draw the graphs of the mathematical statements.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/121207.jpg\"><BR>\n" );
document.write( "3. How will you determine the amount of savings in each bank account?<BR>\n" );
document.write( "the graph shows the opposite of the constraint inequalities.<BR>\n" );
document.write( "x + y >= 150,000 is graphed as x + y <= 150,000.<BR>\n" );
document.write( ".04x + .06y <= 12000 is graphed as .04x + .06y >= 12000.<BR>\n" );
document.write( "x >= 0 is graphed as x <= 0.<BR>\n" );
document.write( "y >= 0 is graphed as y <= 0.<BR>\n" );
document.write( "the area of the graph that is NOT SHADED is the region of fesibility.<BR>\n" );
document.write( "all coordinate points within this region are valid and satisfy all the constraints.<BR>\n" );
document.write( "4. Give one possible amount of savings in both accounts.<BR>\n" );
document.write( "one coordinate point would be (300,000,0).<BR>\n" );
document.write( "this means all the investments yield 4% interest.<BR>\n" );
document.write( "if the interest was 12,000, then the amount invested had to be 12,000 / .04 = 300,000.<BR>\n" );
document.write( "another point within the feasible region would be (100,000,100,000).<BR>\n" );
document.write( "the amount invested would be 200,000 which is greater than 150,000.<BR>\n" );
document.write( "the interest would be .04 * 100,000 + .06 * 100,000 = 10,000 which is less than 12,000.<BR>\n" );
document.write( "a point outside the feasible region would be (150,000,200,000).<BR>\n" );
document.write( "the amount invested is equal to 350,000 which is greater than 150,000.<BR>\n" );
document.write( "the interest would be .04 * 150,000 + .06 * 200,000 = 18,000 which is NOT less than 12,000.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );