QuestionA sandwich shop has a weekly cost of \$515 and variable costs of \$0.55 per roast beef sandwich.
a. Write the cost function $C(x)=515.00+0.55 x$ .
b. The revenue function is $R(x)=-0.001 x^{2}+3 x$ . Write the profit function $P(x)=R(x)-C(x)$ . Simplify your answer.

Studdy Solution

STEP 1

Assumptions1. The fixed weekly cost is \ $515.00. The variable cost per roast beef sandwich is \$0.553. The number of roast beef sandwiches made and sold each week is represented by$ x $<br />4. The weekly cost function is represented by$ C(x) $5. The revenue function is represented by$ R(x) $6. The profit function is represented by$ (x)$

STEP 2

We are asked to write the weekly cost function, $C$ , for the local sandwich store. This function is a sum of the fixed cost and the variable cost multiplied by the number of sandwiches sold.
$C(x) = Fixed\, cost + Variable\, cost \times x$

STEP 3

Now, plug in the given values for the fixed cost and variable cost to write the cost function.
$C(x) = \$515.00 + \$0.55 \times x$

STEP 4

The cost function is now written as $C(x) =515.00 +0.55x$

STEP 5

The function $R(x)=-0.001 x^{2}+3 x$ describes the money that the local sandwich store takes in each week from the sale of $x$ roast beef sandwiches. We are asked to write the store's weekly profit function, $(x)$ , which is the difference between the revenue and cost functions.
$(x) = R(x) - C(x)$

STEP 6

Now, plug in the given values for the revenue function $R(x)$ and cost function $C(x)$ to write the profit function.
$(x) = (-0.001 x^{2}+3 x) - (515.00 +0.55x)$

STEP 7

implify the profit function by combining like terms.
$(x) = -0.001 x^{2} +3x -0.55x -515.00$

STEP 8

The profit function is now written as $(x) = -0.001 x^{2} +2.45x -515.00$ The local sandwich store's weekly profit function is $(x) = -0.001 x^{2} +2.45x -515.00$ .

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QuestionA sandwich shop has a weekly cost of \$515 and variable costs of \$0.55 per roast beef sandwich.
a. Write the cost function $C(x)=515.00+0.55 x$ .
b. The revenue function is $R(x)=-0.001 x^{2}+3 x$ . Write the profit function $P(x)=R(x)-C(x)$ . Simplify your answer.

Studdy Solution

STEP 1

STEP 2

We are asked to write the weekly cost function, $C$ , for the local sandwich store. This function is a sum of the fixed cost and the variable cost multiplied by the number of sandwiches sold.
$C(x) = Fixed\, cost + Variable\, cost \times x$

STEP 3

Now, plug in the given values for the fixed cost and variable cost to write the cost function.
$C(x) = \$515.00 + \$0.55 \times x$

STEP 4

The cost function is now written as $C(x) =515.00 +0.55x$

STEP 5

The function $R(x)=-0.001 x^{2}+3 x$ describes the money that the local sandwich store takes in each week from the sale of $x$ roast beef sandwiches. We are asked to write the store's weekly profit function, $(x)$ , which is the difference between the revenue and cost functions.
$(x) = R(x) - C(x)$

STEP 6

Now, plug in the given values for the revenue function $R(x)$ and cost function $C(x)$ to write the profit function.
$(x) = (-0.001 x^{2}+3 x) - (515.00 +0.55x)$

STEP 7

implify the profit function by combining like terms.
$(x) = -0.001 x^{2} +3x -0.55x -515.00$

STEP 8

The profit function is now written as $(x) = -0.001 x^{2} +2.45x -515.00$ The local sandwich store's weekly profit function is $(x) = -0.001 x^{2} +2.45x -515.00$ .

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Studdy Solution

STEP 1

STEP 2

We are asked to write the weekly cost function, CCC, for the local sandwich store. This function is a sum of the fixed cost and the variable cost multiplied by the number of sandwiches sold.C(x)=Fixed cost+Variable cost×xC(x) = Fixed\, cost + Variable\, cost \times xC(x)=Fixedcost+Variablecost×x

STEP 3

Now, plug in the given values for the fixed cost and variable cost to write the cost function.C(x)=$515.00+$0.55×xC(x) = \$515.00 + \$0.55 \times xC(x)=$515.00+$0.55×x

STEP 4

The cost function is now written asC(x)=515.00+0.55xC(x) =515.00 +0.55xC(x)=515.00+0.55x

STEP 5

STEP 6

Now, plug in the given values for the revenue function R(x)R(x)R(x) and cost function C(x)C(x)C(x) to write the profit function.(x)=(−0.001x2+3x)−(515.00+0.55x)(x) = (-0.001 x^{2}+3 x) - (515.00 +0.55x)(x)=(−0.001x2+3x)−(515.00+0.55x)

STEP 7

implify the profit function by combining like terms.(x)=−0.001x2+3x−0.55x−515.00(x) = -0.001 x^{2} +3x -0.55x -515.00(x)=−0.001x2+3x−0.55x−515.00

STEP 8

The profit function is now written as(x)=−0.001x2+2.45x−515.00(x) = -0.001 x^{2} +2.45x -515.00(x)=−0.001x2+2.45x−515.00The local sandwich store's weekly profit function is (x)=−0.001x2+2.45x−515.00(x) = -0.001 x^{2} +2.45x -515.00(x)=−0.001x2+2.45x−515.00.

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We are asked to write the weekly cost function, $C$ , for the local sandwich store. This function is a sum of the fixed cost and the variable cost multiplied by the number of sandwiches sold.
$C(x) = Fixed\, cost + Variable\, cost \times x$

Now, plug in the given values for the fixed cost and variable cost to write the cost function.
$C(x) = \$515.00 + \$0.55 \times x$

The cost function is now written as $C(x) =515.00 +0.55x$

Now, plug in the given values for the revenue function $R(x)$ and cost function $C(x)$ to write the profit function.
$(x) = (-0.001 x^{2}+3 x) - (515.00 +0.55x)$

implify the profit function by combining like terms.
$(x) = -0.001 x^{2} +3x -0.55x -515.00$

The profit function is now written as $(x) = -0.001 x^{2} +2.45x -515.00$ The local sandwich store's weekly profit function is $(x) = -0.001 x^{2} +2.45x -515.00$ .