Problema Solution
the total sales in dollars of some small business fluctuates according to the equation S=A+B sinπx/6, where x is the number in months, with x=1 corresponding to January, A= 6700, and B= 4000. Determine the month with the greatest total sales and give the sales in that month
Answer provided by our tutors
S=A+B sinπx/6, where x is the number in months, with x=1 corresponding to January, A= 6700, and B= 4000
S=6700+4000*sinπx/6
sinπx/6 has maximum for πx/6 = π/2 + 2kπ, k is constant (when sinπx/6 = 1)
πx/6 = π/2 + 2kπ divide both sides by π/6
x = 3 + 12k, k is constant
for k = 0 we have x = 3 the month is March and the total sale for that month is S = 6700+4000*sin(π*3/6) = 6700 + 4000 = $10,700.