at the beginning of january, kesia records paid $148,950 to acquire the exclusive rights to a new album. it…

at the beginning of january, kesia records paid $148,950 to acquire the exclusive rights to a new album. it costs them $1.13 to print a copy of this album, which they can sell for $9.75. the following chart shows the sales of that record, along with the overhead expenses of running a record studio, not counting production costs. month albums sold expenses jan. 5,486 $27,714 feb. 8,191 $21,689 mar. 4,796 $25,195 apr. 7,490 $28,766 may 6,272 $24,604 jun. 5,131 $29,040 in which month did kesia records first break even? a. january b. march c. april d. may

at the beginning of january, kesia records paid $148,950 to acquire the exclusive rights to a new album. it costs them $1.13 to print a copy of this album, which they can sell for $9.75. the following chart shows the sales of that record, along with the overhead expenses of running a record studio, not counting production costs. month albums sold expenses jan. 5,486 $27,714 feb. 8,191 $21,689 mar. 4,796 $25,195 apr. 7,490 $28,766 may 6,272 $24,604 jun. 5,131 $29,040 in which month did kesia records first break even? a. january b. march c. april d. may

Answer

Explanation:

Step1: Calculate profit - formula

Let $n$ be the number of albums sold. The cost function $C$ is the sum of the acquisition cost, production cost and overhead expenses. The acquisition cost is $148950$, the production cost per - album is $1.13n$, and the overhead expense for each month is given in the table. The revenue function $R = 9.75n$. The profit function $P=R - C=9.75n-(148950 + 1.13n+ \text{Overhead})=8.62n-(148950+\text{Overhead})$.

Step2: Calculate profit for January

For January, $n = 5486$ and overhead $=27714$. $P_1=8.62\times5486-(148950 + 27714)$ $P_1=8.62\times5486-176664$ $P_1 = 47299.32-176664=- 129364.68$

Step3: Calculate profit for February

For February, $n = 8191$ and overhead $=21689$. $P_2=8.62\times8191-(148950 + 21689)$ $P_2=70606.42-170639=-99932.58$

Step4: Calculate profit for March

For March, $n = 4796$ and overhead $=25195$. $P_3=8.62\times4796-(148950 + 25195)$ $P_3=41341.52-174145=-132803.48$

Step5: Calculate profit for April

For April, $n = 7490$ and overhead $=28766$. $P_4=8.62\times7490-(148950 + 28766)$ $P_4=64563.8-177716=-113152.2$

Step6: Calculate profit for May

For May, $n = 6272$ and overhead $=24604$. $P_5=8.62\times6272-(148950 + 24604)$ $P_5=54064.64-173554=-119489.36$

Step7: Calculate cumulative sales and profit

We can also calculate cumulative sales and profit. Let's calculate cumulative number of albums sold and cumulative overheads month - by - month. Cumulative number of albums sold until January: $n_1 = 5486$ Cumulative overhead until January: $O_1=27714$ $P_{cum1}=8.62\times5486-(148950 + 27714)=-129364.68$ Cumulative number of albums sold until February: $n_2=5486 + 8191=13677$ Cumulative overhead until February: $O_2=27714+21689 = 49403$ $P_{cum2}=8.62\times13677-(148950 + 49403)$ $P_{cum2}=117995.74-198353=-80357.26$ Cumulative number of albums sold until March: $n_3=13677+4796 = 18473$ Cumulative overhead until March: $O_3=49403+25195 = 74598$ $P_{cum3}=8.62\times18473-(148950 + 74598)$ $P_{cum3}=159237.26-223548=-64310.74$ Cumulative number of albums sold until April: $n_4=18473+7490 = 25963$ Cumulative overhead until April: $O_4=74598+28766 = 103364$ $P_{cum4}=8.62\times25963-(148950 + 103364)$ $P_{cum4}=223700.06-252314=-28613.94$ Cumulative number of albums sold until May: $n_5=25963+6272 = 32235$ Cumulative overhead until May: $O_5=103364+24604 = 127968$ $P_{cum5}=8.62\times32235-(148950 + 127968)$ $P_{cum5}=277865.7-276918 = 947.7$

Answer:

d. May