Questiona. Define the weekly cost function $C(x)=530.00+0.60 x$ for sandwiches sold. b. Find the profit function $P(x)$ using $R(x)=-0.001 x^{2}+3 x$ . $P(x)=R(x)-C(x)$

Studdy Solution

STEP 1

Assumptions1. $x$ represents the number of roast beef sandwiches made and sold each week. . The weekly cost function for the local sandwich store is $C(x)=530.00+0.60x$ .
3. The weekly revenue function for the local sandwich store is $R(x)=-0.001x^{}+3x$ .
4. The profit function, $(x)$ , is the difference between the revenue function and the cost function.

STEP 2

The profit function is the difference between the revenue function and the cost function. We can write this as $(x) = R(x) - C(x)$

STEP 3

Now, plug in the given functions for $R(x)$ and $C(x)$ into the equation for $(x)$ .
$(x) = (-0.001x^{2}+3x) - (530.00+0.60x)$

STEP 4

implify the equation by distributing the negative sign on the right side of the equation.
$(x) = -0.001x^{2}+3x -530.00 -0.60x$

STEP 5

Combine like terms to simplify the equation further.
$(x) = -0.001x^{2} + (3 -0.60)x -530.00$

STEP 6

implify the coefficients of $x$ .
$(x) = -0.001x^{2} +2.4x -530.00$ So, the store's weekly profit function, $(x)$ , is $-0.001x^{2} +2.4x -530.00$ .

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Questiona. Define the weekly cost function $C(x)=530.00+0.60 x$ for sandwiches sold. b. Find the profit function $P(x)$ using $R(x)=-0.001 x^{2}+3 x$ . $P(x)=R(x)-C(x)$

Studdy Solution

STEP 1

STEP 2

The profit function is the difference between the revenue function and the cost function. We can write this as $(x) = R(x) - C(x)$

STEP 3

Now, plug in the given functions for $R(x)$ and $C(x)$ into the equation for $(x)$ .
$(x) = (-0.001x^{2}+3x) - (530.00+0.60x)$

STEP 4

implify the equation by distributing the negative sign on the right side of the equation.
$(x) = -0.001x^{2}+3x -530.00 -0.60x$

STEP 5

Combine like terms to simplify the equation further.
$(x) = -0.001x^{2} + (3 -0.60)x -530.00$

STEP 6

implify the coefficients of $x$ .
$(x) = -0.001x^{2} +2.4x -530.00$ So, the store's weekly profit function, $(x)$ , is $-0.001x^{2} +2.4x -530.00$ .

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Questiona. Define the weekly cost function C(x)=530.00+0.60xC(x)=530.00+0.60 xC(x)=530.00+0.60x for sandwiches sold. b. Find the profit function P(x)P(x)P(x) using R(x)=−0.001x2+3xR(x)=-0.001 x^{2}+3 xR(x)=−0.001x2+3x. P(x)=R(x)−C(x)P(x)=R(x)-C(x)P(x)=R(x)−C(x)

Studdy Solution

STEP 1

STEP 2

The profit function is the difference between the revenue function and the cost function. We can write this as(x)=R(x)−C(x)(x) = R(x) - C(x)(x)=R(x)−C(x)

STEP 3

Now, plug in the given functions for R(x)R(x)R(x) and C(x)C(x)C(x) into the equation for (x)(x)(x).(x)=(−0.001x2+3x)−(530.00+0.60x)(x) = (-0.001x^{2}+3x) - (530.00+0.60x)(x)=(−0.001x2+3x)−(530.00+0.60x)

STEP 4

implify the equation by distributing the negative sign on the right side of the equation.(x)=−0.001x2+3x−530.00−0.60x(x) = -0.001x^{2}+3x -530.00 -0.60x(x)=−0.001x2+3x−530.00−0.60x

STEP 5

Combine like terms to simplify the equation further.(x)=−0.001x2+(3−0.60)x−530.00(x) = -0.001x^{2} + (3 -0.60)x -530.00(x)=−0.001x2+(3−0.60)x−530.00

STEP 6

implify the coefficients of xxx.(x)=−0.001x2+2.4x−530.00(x) = -0.001x^{2} +2.4x -530.00(x)=−0.001x2+2.4x−530.00So, the store's weekly profit function, (x)(x)(x), is −0.001x2+2.4x−530.00-0.001x^{2} +2.4x -530.00−0.001x2+2.4x−530.00.

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Questiona. Define the weekly cost function $C(x)=530.00+0.60 x$ for sandwiches sold. b. Find the profit function $P(x)$ using $R(x)=-0.001 x^{2}+3 x$ . $P(x)=R(x)-C(x)$

The profit function is the difference between the revenue function and the cost function. We can write this as $(x) = R(x) - C(x)$

Now, plug in the given functions for $R(x)$ and $C(x)$ into the equation for $(x)$ .
$(x) = (-0.001x^{2}+3x) - (530.00+0.60x)$

implify the equation by distributing the negative sign on the right side of the equation.
$(x) = -0.001x^{2}+3x -530.00 -0.60x$

Combine like terms to simplify the equation further.
$(x) = -0.001x^{2} + (3 -0.60)x -530.00$

implify the coefficients of $x$ .
$(x) = -0.001x^{2} +2.4x -530.00$ So, the store's weekly profit function, $(x)$ , is $-0.001x^{2} +2.4x -530.00$ .