assume that the following has a linear cost function.\n|fixed cost|marginal cost per item|item sells…

assume that the following has a linear cost function.\n|fixed cost|marginal cost per item|item sells for|\n|$600|$12|$35|\nfind the following.\n(a) the cost function\n(b) the revenue function\n(c) the profit function\n(d) the profit on 96 items\n\n(a) the cost function is c(x) = .\n(simplify your answer. do not include the $ symbol in your answer.)

assume that the following has a linear cost function.\n|fixed cost|marginal cost per item|item sells for|\n|$600|$12|$35|\nfind the following.\n(a) the cost function\n(b) the revenue function\n(c) the profit function\n(d) the profit on 96 items\n\n(a) the cost function is c(x) = .\n(simplify your answer. do not include the $ symbol in your answer.)

Answer

Explanation:

Step1: Recall cost - function formula

The linear cost function is of the form $C(x)=FC + MC\times x$, where $FC$ is the fixed cost and $MC$ is the marginal cost per item, and $x$ is the number of items. Given $FC = 600$ and $MC=12$, so $C(x)=600 + 12x$.

Step2: Recall revenue - function formula

The revenue function $R(x)$ is given by the selling - price per item times the number of items. Given the item sells for $35$ per item, so $R(x)=35x$.

Step3: Recall profit - function formula

The profit function $P(x)$ is $P(x)=R(x)-C(x)$. Substitute $R(x)=35x$ and $C(x)=600 + 12x$ into the formula: $P(x)=35x-(600 + 12x)=35x-600 - 12x=23x-600$.

Step4: Calculate profit for 96 items

Substitute $x = 96$ into the profit function $P(x)$. $P(96)=23\times96-600$. First, calculate $23\times96 = 23\times(100 - 4)=2300-92 = 2208$. Then $P(96)=2208-600=1608$.

Answer:

(a) $600 + 12x$ (b) $35x$ (c) $23x-600$ (d) $1608$