document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181961>Question 1181961</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	A financial advisor at Diehl Investments identified two companies that are likely candidates for a takeover in the near future. Eastern Cable is a leading manufacturer of flexible cable systems used in the construction industry, and ComSwitch is a new firm specializing in digital switching systems. Eastern Cable is currently trading for $40 per share, and ComSwitch is currently trading for $25 per share. If the takeovers occur, the financial advisor estimates that the price of Eastern Cable will go to $55 per share and ComSwitch will go to $43 per share. At this point in time, the financial advisor has identified ComSwitch as the higher-risk alternative. Assume that a client indicated a willingness to invest a maximum of $50,000 in the two companies. The client wants to invest at least $15,000 in Eastern Cable and at least $10,000 in ComSwitch. Because of the higher risk associated with ComSwitch, the financial advisor has recommended that at most $25,000 should be invested in ComSwitch. <BR>\n" );
document.write( "A.	. Formulate a linear programming model that can be used to determine the number of shares of Eastern Cable and the number of shares of ComSwitch that will meet the investment constraints and maximize the total return for the investment <BR>\n" );
document.write( "B.	Solve the problem  using simplex method <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851880 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "1.	A financial advisor at Diehl Investments identified two companies that are likely candidates for a takeover in the near future. Eastern Cable is a leading manufacturer of flexible cable systems used in the construction industry, and ComSwitch is a new firm specializing in digital switching systems. Eastern Cable is currently trading for $40 per share, and ComSwitch is currently trading for $25 per share. If the takeovers occur, the financial advisor estimates that the price of Eastern Cable will go to $55 per share and ComSwitch will go to $43 per share. At this point in time, the financial advisor has identified ComSwitch as the higher-risk alternative. Assume that a client indicated a willingness to invest a maximum of $50,000 in the two companies. The client wants to invest at least $15,000 in Eastern Cable and at least $10,000 in ComSwitch. Because of the higher risk associated with ComSwitch, the financial advisor has recommended that at most $25,000 should be invested in ComSwitch. <BR>\n" );
document.write( "A.	. Formulate a linear programming model that can be used to determine the number of shares of Eastern Cable and the number of shares of ComSwitch that will meet the investment constraints and maximize the total return for the investment <BR>\n" );
document.write( "B.	Solve the problem  using simplex method <BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This problem is &nbsp;SO &nbsp;SIMPLE &nbsp;that can be solved &nbsp;MENTALLY, \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;using common sense &nbsp;ONLY &nbsp;and no other special methods.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Here's the solution:\r\n" );
document.write( "\r\n" );
document.write( "**A. Linear Programming Model**\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "*   **Decision Variables:**\r\n" );
document.write( "    *   x = Number of shares of Eastern Cable\r\n" );
document.write( "    *   y = Number of shares of ComSwitch\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "*   **Objective Function (Maximize Return):**\r\n" );
document.write( "    *   Maximize Z = (55-40)x + (43-25)y = 15x + 18y\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "*   **Constraints:**\r\n" );
document.write( "    *   Total Investment: 40x + 25y ≤ 50000                              (1)\r\n" );
document.write( "    *   Minimum Eastern Cable Investment: 40x ≥ 15000  => x ≥ 375        (2)\r\n" );
document.write( "    *   Minimum ComSwitch Investment: 25y ≥ 10000 => y ≥ 400             (3)\r\n" );
document.write( "    *   Maximum ComSwitch Investment: 25y ≤ 25000 => y ≤ 1000            (4)\r\n" );
document.write( "    *   Non-negativity: x ≥ 0, y ≥ 0                                     (5)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "**B. Solving MENTALLY using COMMON SENSE**\r\n" );
document.write( "\r\n" );
document.write( "    Looking into the objective function  Z = 15x + 18y,  you see that getting great values of 'y' is most profitable.\r\n" );
document.write( "\r\n" );
document.write( "    So, the most aggressive strategy is to take 'y' as great as possible (1000, as allowed by constraint (4))\r\n" );
document.write( "    and then to take 'x' as big as allowed by other constraints (1) and (2).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Constraint (1) gives x >= 375;  constraint (2) gives  x <= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850000-25%2A1000%29%2F40 ALIGN=MIDDLE  ALT=\"%2850000-25%2A1000%29%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 625.\r\n" );
document.write( "\r\n" );
document.write( "    So, we take  x = 625,  y = 1000.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Then all constraints are satisfied, and we get maximum return  15*625 + 18*1000 = 27375.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "<U>ANSWER</U>.  The optimum strategy is 625 Eastern Cable shares and 1000 ComSwitch shares,\r\n" );
document.write( "\r\n" );
document.write( "         providing the maximum possible return of $27375.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "Solved mentally.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-----------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<H3>Post-solution note</H3>\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This problem is a typical &nbsp;\" FALSE &nbsp;Linear &nbsp;Programming problem \".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;First impression is that it is a Linear programming problem,\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;but when you write constraints and think &nbsp;1 - 2 - 3 &nbsp;minutes,\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;you will find a &nbsp;MENTAL &nbsp;SOLUTION.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;By knowing this approach, &nbsp;you may impress your teacher/professor, \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;may get &nbsp;5++ &nbsp;at exam and successfully pass a job interview to the applause of the interviewers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );