Question

A small company markets a new multi-vitamin. The function S(p) = 1.5(−p² + 1600p) predicts the total sales S as a function of the price p of one jar of the the multi- vitamin. Predict the total sales if each jar of the multi-vitamin is priced at $12.

A. $36,281
B. $28,584
C. $41,472
D. $18,419

Answer 1

The correct answer is option $36,281. To predict the total sales when the price of the multi-vitamin is $12, substitute the value into the function S(p) = 1.5(−p² + 1600p).

Step-by-step explanation:

The correct answer is option A. $36,281.

To predict the total sales when each jar of the multi-vitamin is priced at $12, we substitute p = 12 into the function S(p) = 1.5(−p² + 1600p).

S(12) = 1.5(−12² + 1600(12))

S(12) = 1.5(−144 + 19200)

S(12) = 1.5(19056)

S(12) = 28608

Hence, the predicted total sales is $36,281.

To predict the total sales if each jar of the multi-vitamin is priced at $12, we substitute the price p into the sales function S(p). The function given is S(p) = 1.5(−p² + 1600p). Performing the substitution, we get S(12) = 1.5(−12² + 1600*12). Calculation yields S(12) = 1.5(−144 + 19200) which simplifies to S(12) = 1.5(19056). Therefore, the total sales for the multi-vitamin priced at $12 is S(12) = 28584.