Math

QuestionRevenue from selling xx hundred cell phones is R(x)=1.9x2+323xR(x)=-1.9x^2+323x. Cost is C(x)=0.09x32x2+75x+600C(x)=0.09x^3-2x^2+75x+600. Find profit P(x)=R(x)C(x)P(x)=R(x)-C(x), then compute P(25)P(25). Interpret P(25)P(25).

Studdy Solution

STEP 1

Assumptions1. The revenue function is R(x)=1.9x+323xR(x)=-1.9 x^{}+323 x . The cost function is C(x)=0.09x3x+75x+600C(x)=0.09 x^{3}- x^{}+75 x+600
3. The profit function is defined as (x)=R(x)C(x)(x)=R(x)-C(x)4. The number of cell phones sold, xx, is in hundreds.

STEP 2

We need to find the profit function, (x)(x), by subtracting the cost function, C(x)C(x), from the revenue function, R(x)R(x).
(x)=R(x)C(x)(x)=R(x)-C(x)

STEP 3

Substitute the given functions R(x)R(x) and C(x)C(x) into the equation.
(x)=(1.9x2+323x)(0.09x32x2+75x+600)(x)=(-1.9 x^{2}+323 x) - (0.09 x^{3}-2 x^{2}+75 x+600)

STEP 4

istribute the negative sign to all the terms in the brackets.
(x)=1.9x2+323x0.09x3+2x275x600(x)=-1.9 x^{2}+323 x -0.09 x^{3}+2 x^{2}-75 x-600

STEP 5

Rearrange the terms in descending order of power.
(x)=0.09x3+0.1x2+248x600(x)=-0.09 x^{3}+0.1 x^{2}+248 x-600

STEP 6

Now, we need to find the profit if x=25x=25 hundred cell phones are sold. Substitute x=25x=25 into the profit function (x)(x).
(25)=0.09(25)3+0.1(25)2+248(25)600(25)=-0.09 (25)^{3}+0.1 (25)^{2}+248 (25)-600

STEP 7

Calculate the profit when x=25x=25.
(25)=0.09(25)3+0.1(25)2+248(25)600=4875(25)=-0.09 (25)^{3}+0.1 (25)^{2}+248 (25)-600 =4875So, the profit when x=25x=25 hundred cell phones are sold is $4875.

STEP 8

Interpretation of (25)(25) This means that when2500 cell phones are sold, the profit made is $4875.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord