the revenue that an apparel company earns each month for its different product lines fluctuates throughout…
the revenue that an apparel company earns each month for its different product lines fluctuates throughout the year. over the course of a year, the revenue earned from clothing sales each month is modeled by function c, where x is the number of months since the beginning of the year. the revenue earned from sales of shoes and accessories each month is modeled by function s, where x is the number of months since the beginning of the year. s(x)=0.6x³ - 10.2x² + 32.4x + 127.2 use this information to complete the statement. between the 3rd and 6th months, the revenue earned from sales of shoes and accessories is at the revenue earned from sales of clothing.
Answer
Explanation:
Step1: Find the revenue from shoe - and - accessory sales at (x = 3)
Substitute (x = 3) into (s(x)=0.6x^{3}-10.2x^{2}+32.4x + 127.2). [ \begin{align*} s(3)&=0.6\times3^{3}-10.2\times3^{2}+32.4\times3 + 127.2\ &=0.6\times27-10.2\times9 + 97.2+127.2\ &=16.2-91.8+97.2 + 127.2\ &=(16.2+97.2+127.2)-91.8\ &=240.6 - 91.8\ &=148.8 \end{align*} ]
Step2: Find the revenue from shoe - and - accessory sales at (x = 6)
Substitute (x = 6) into (s(x)=0.6x^{3}-10.2x^{2}+32.4x + 127.2). [ \begin{align*} s(6)&=0.6\times6^{3}-10.2\times6^{2}+32.4\times6+127.2\ &=0.6\times216-10.2\times36 + 194.4+127.2\ &=129.6-367.2+194.4 + 127.2\ &=(129.6+194.4+127.2)-367.2\ &=451.2-367.2\ &=84 \end{align*} ] Since (s(3)=148.8) and (s(6)=84), the revenue from sales of shoes and accessories is decreasing between the 3rd and 6th months. Now, from the graph of (c(x)), when (x = 3), (c(3)\approx120) and when (x = 6), (c(6)\approx80). We can see that between the 3rd and 6th months, the revenue from sales of shoes and accessories is decreasing at a greater rate than the revenue from sales of clothing.