A manufacturer of 24-hr variable timers, has a mounthly fixed cost of $ 45 , 000 and a production cost of $ 8 for each timer manufactured. The units sell for $ 13 eacha) Graph the cost and revenue functions.b) Find the break-even point. ( x , y ) = ?c) Graph the point function.d) At what point does the graph of the profit function cross the x-axis? ( x , y ) = ?

Question

A manufacturer of 24-hr variable timers, has a mounthly fixed cost of   $  45  ,  000 and a production cost of   $  8 for each timer manufactured. The units sell for   $  13 eacha) Graph the cost and revenue functions.b) Find the break-even point.  (  x  ,     y  )  =  ?c) Graph the point function.d) At what point does the graph of the profit function cross the x-axis?  (  x  ,     y  )  =  ?

volksgeesr9 · Accepted Answer

Step 1We will take no. of units. produced on X axis and Amount in       $   on Y axisFixed cost will be parallel line to X- axis as it is constant throughout and above the X - axisThe line of total cost would start from the point where the line of fixed cost meets the Y - axis.The line of sales revenue would start from origin (0,0) and move upwardThe point where these two lines will intersect will be break even point in units.  Total variable cost  =  variable cost per unit  ×  no. of units&amp;gt;br?  Revenue  =  selling price per unit  ×  no. of units  total cost  =  fixed cost  +  variable cost                    Units                    Fixed cost                    Variable cost                    Total cost                    revenue                            1000                    45000                    5000                    50000                    13000                            2000                    45000                    10000                    55000                    26000                            3000                    45000                    15000                    60000                    39000                            4000                    45000                    20000                    65000                    52000                            5000                    45000                    25000                    70000                    65000                            6000                    45000                    30000                    75000                    78000                            7000                    45000                    35000                    80000                    91000                            8000                    45000                    40000                    85000                    104000                            9000                    45000                    45000                    90000                    117000                            10000                    45000                    50000                    95000                    130000                            11000                    45000                    55000                    100000                    143000            Step 2b) Break even point is where revenue and total cost intersect which is at point (6000, 78000) break even units is 6000 units and break even in sales is   $  78000 .

fotaczkak4 · Accepted Answer

Step 1Calculating profit as revenue - total cost                    Total cost                    revenue                    profit                            50000                    13000                    −        37000                            55000                    26000                    −        29000                            60000                    39000                    −        21000                            65000                    52000                    −        13000                            70000                    65000                    −        5000                            75000                    78000                    3000                            80000                    91000                    11000                            85000                    104000                    19000                            90000                    117000                    27000                            95000                    130000                    35000                            100000                    143000                    43000            d) Profit will start coming after the sale of 78000 unitsSo profit function cross x - axis at (0,7800)

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