CHAPTER 3 THE CONCEPTUAL PAPER WORKSHEET To solve the Break-Even Model Through a table of relevant data, finding the answer where PROFIT is exactly zero. Through a graphical representation of the relevant data, finding the answer from the graph. Through a system of linear simultaneous equations, finding the answer by solving the system of linear equations.

CONCEPTUAL PAPER WORKSHEET (CPW) To highlight the important modelling and package handling issues The construction of a CPW is useful in three ways : To clarify any academic modelling issues. To determine the size of the worksheet and the range of cells that will be used. To identifies the range of package facilities that will need to be activated in constructing the model through a worksheet.

WHAT IS A WORKSHEET ? A large two dimensional piece of paper COLUMNS---LETTER LABELS ROWS--- NUMBER LABELS CELL/BOX---combination of COLUMN and ROW Example Table 3.1 On WORKSHEET, the user enters instructions that enable the package to perform relevant data manipulations. Two software packages The SPREADSHEET package EXCEL To be controlled through MENUS The STATISTICAL package MNITAB To be controlled through COMMANDS

User inputs of CPW A clear specification of the academic issues (THE THEORETICAL MODEL ) Is the problem properly defined? Is the model properly structured? Are all the variables required specified? Are the variables of interest properly defined? Explicit recognition of the package handling facilities(BUILDING A WORKSHEET )

SECTION I: CREATING A TABLE OF DATA Four inputs into the Break-Even model SELLING PRICE per unit (p), FIXED COSTS (FC), VARIABLE COST per unit (VC), and RANGE of OUTPUTS q---quantity to produce To determine SIZE of the worksheet to be created.

BASIC INPUTS A1—A23 (Table 3.2) Cell A9: FORMULA : =A8+10 '=' means that this cell input is a formula and not a label or a number COPY the IDEA CONTAINED in A9 INTO A10 and then ALL THE WAY THROUGH TO A23. TOTAL REVENUE COLUMN B7—TR cell B8: FORMULA : =$B$3*A8 PRICExQUANTITY $--RELATIVE and an ABSOLUTE CELL ADDRESS. X is replaced by * COPY the idea contained in B8 into the cells B9 THROUGH TO B23

TOTAL COST COLUMN C7—TC C8: FORMULA : =$B$4+$B$5*A8 TC = FC + VCq COPY the idea contained in C8 into the cells C9 THROUGH TO C23 PROFIT D7—PROFIT D8: FORMULA : =B8-C8 Copy the FORMULA in cell D8 into D9 THROUGH TO D23

FILE HANDLING FACILITIES, FILE/SAVE FILE/OPEN SUMMRY DATA ENTRY : entering both labels/names and formula COPYING : to copy a formula to other FILE HANDLING : to save and retrieve the worksheet

SECTION II: WORKSHEET GRAPHS What kind of graph is to be constructed? pie charts, bar graphs, X-Y graph,… What is to measured along the X-axis? Q– quantity produced What is to be measured up the Y-axis? TR, TC and PROFIT Labelling the Lines (TR, TC and PROFIT )

Graph Titles Break-Even Analysis Scaling of Axes

SECTION III: GENERATING A NUMERICAL SOLUTION Matrix A and Matrix b E1—E4: TR F1—F4: TC G1—G4: q Matrix A is in the range E2 to G4

H1—H4: RHS Matrix b is in the range H2 to H4 Where to put the answer? J1—J4: ANSWER To generate the answer by the following steps: inform the package as to the whereabouts of the matrix A. inform the package that we would like to form the inverse of A, A -1.

inform the package where in the spreadsheet we would like to store the inverse matrix A -1 inform the package as to the whereabouts of the matrix b inform the package that we would like to perform the multiplication A -1 b inform the package where we would like the answer to be displayed