Pinewood Furniture Company

Pin" rel="nofollow">inewood Furniture Company produces chairs and tables from two resources----labor and wood. The company has 80 hours of labor and 36 board -ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hoursof labor and 6 board-ft. of wood. The profit derived from each chair is $400 and fromeach table $100. The company wants to determin" rel="nofollow">ine the number of chairs and tables to produce each day in" rel="nofollow">in order to maximize profit.(Please note that RHS sensitivity can be applied to ALL constrain" rel="nofollow">ints, in" rel="nofollow">includin" rel="nofollow">ing the non-bin" rel="nofollow">indin" rel="nofollow">ing constrain" rel="nofollow">ints. A non-bin" rel="nofollow">indin" rel="nofollow">ing constrain" rel="nofollow">ints usually has either a lower bound at negative in" rel="nofollow">infin" rel="nofollow">inity and an actual upper bound when it passes through the origin" rel="nofollow">inal optimal solution, or an upper bound at positive in" rel="nofollow">infin" rel="nofollow">inity and an actual lower bound when it passes through the origin" rel="nofollow">inal optimal solution. To fin" rel="nofollow">ind the fin" rel="nofollow">inite bound for a non-bin" rel="nofollow">indin" rel="nofollow">ing constrain" rel="nofollow">int (when it passes through the origin" rel="nofollow">inal optimal solution), you can plug in" rel="nofollow">in the coordin" rel="nofollow">inates of the origin" rel="nofollow">inal optimal solution in" rel="nofollow">in the left-hand-side of the constrain" rel="nofollow">int to calculate the correspondin" rel="nofollow">ing right-hand-side value. The shadow price for a non-bin" rel="nofollow">indin" rel="nofollow">ing constrain" rel="nofollow">int is always zero, and it would be sufficient to simply express this fact in" rel="nofollow">in your homework answers.) Question: 1 - Develop a lin" rel="nofollow">inear programmin" rel="nofollow">ing model (CH2): Defin" rel="nofollow">ine each decision variable, in" rel="nofollow">include the objective function, and in" rel="nofollow">include all constrain" rel="nofollow">ints, together with the non-negativity constrain" rel="nofollow">ints. Put a one to two word explanation next to each constrain" rel="nofollow">int to identify each constrain" rel="nofollow">int’s role. 2 - Solve the lin" rel="nofollow">inear program graphically (CH2): On a separate page, draw the graph clearly usin" rel="nofollow">ing the entire page (you can use graphin" rel="nofollow">ing paper if you prefer). Use a ruler to draw the constrain" rel="nofollow">int lin" rel="nofollow">ines. Show all of your calculations to fin" rel="nofollow">ind the poin" rel="nofollow">ints that constrain" rel="nofollow">ints in" rel="nofollow">intersect with horizontal and vertical axes. Show the feasible region by lightly shadin" rel="nofollow">ing it. Assume one of the vertices of the feasible region to be optimum and draw your objective lin" rel="nofollow">ine passin" rel="nofollow">ing through that poin" rel="nofollow">int. Determin" rel="nofollow">ine the direction of progress and fin" rel="nofollow">ind the last poin" rel="nofollow">int of contact between the objective lin" rel="nofollow">ine and the feasible region as your optimal solution. If the optimal poin" rel="nofollow">int is at an in" rel="nofollow">intersection of two constrain" rel="nofollow">int lin" rel="nofollow">ines, show all of your calculations for solvin" rel="nofollow">ing the system of the two lin" rel="nofollow">inear equations to fin" rel="nofollow">ind the values of optimal solution. Calculate and in" rel="nofollow">include the optimal objective function value. 3 - Fin" rel="nofollow">ind the sensitivity range for the objective function parameters (CH3): On a separate sheet, determin" rel="nofollow">ine the upper bound and lower bound for the slope of the objective function value for which the optimal solution stays the same. Then, fix one objective function parameter at a time and fin" rel="nofollow">ind the correspondin" rel="nofollow">ing upper and lower bounds for the other objective function parameter. See the examples in" rel="nofollow">in the lecture notes. 4 - Fin" rel="nofollow">ind the sensitivity range for the right-hand-side values of the constrain" rel="nofollow">ints (CH3): Determin" rel="nofollow">ine and in" rel="nofollow">include the solution mix and configuration in" rel="nofollow">in terms of zero and non-zero variables. For each constrain" rel="nofollow">int, determin" rel="nofollow">ine when the configuration of the optimal solution change when you in" rel="nofollow">increase and decrease the right-hand-side, and identify these values as the upper and lower bound of the right-side-value of that constrain" rel="nofollow">int. Usin" rel="nofollow">ing these bounds and/or the optimal solution, calculate the shadow price for each constrain" rel="nofollow">int. Show all your work in" rel="nofollow">in detail. See the examples in" rel="nofollow">in the lecture notes and the book. 5 - Solve the lin" rel="nofollow">inear programmin" rel="nofollow">ing model from usin" rel="nofollow">ing Excel Solver (CH3): Format the spreadsheet accordin" rel="nofollow">ing to the examples in" rel="nofollow">in the lecture notes; do NOT use the formattin" rel="nofollow">ing in" rel="nofollow">in the book. Use SUMPRODUCT function to enter formulas for the objective function and the constrain" rel="nofollow">ints (see the examples in" rel="nofollow">in the lecture notes). After solvin" rel="nofollow">ing the problem, create the “answers” and “sensitivity” reports. Prin" rel="nofollow">int out the spreadsheet with your solution on it to a PDF file. Prin" rel="nofollow">int out the same sheet in" rel="nofollow">in formula view (Formulas > Show formulas) to a separate PDF file. Prin" rel="nofollow">int out the sheets with answers and sensitivity reports, each to a different PDF file. Make each prin" rel="nofollow">intout fit within" rel="nofollow">in one page usin" rel="nofollow">ing View > Page Break Preview.