a food truck gyro vendor has weekly fixed costs of $515 and variable costs of $4.70 for each gyro combo…

a food truck gyro vendor has weekly fixed costs of $515 and variable costs of $4.70 for each gyro combo prepared. complete parts a through c below.\n\na. let x represent the number of gyro combos prepared and sold each week. write the weekly cost function, c, for the food truck vendor. (hint: the cost function is the sum of fixed and variable costs.)\nc(x)=515 + 4.7x (use integers or decimals for any numbers in the expression.)\n\nb. the function r(x)= - 0.001x²+8.15x describes the money, in dollars, that the food truck vendor takes in each week from the sale of x gyro combos. use this revenue function and the cost function from part (a) to write the vendors weekly profit function, p. (hint: the profit is the difference between the revenue and the cost functions.)\np(x)= - 0.001x²+8.15x-(515 + 4.7x)= - 0.001x²+3.45x - 515 (simplify your answer. use integers or decimals for any numbers in the expression.)\n\nc. use the vendors profit function to determine the number of gyro combos that should be prepared and sold each week to maximize profit. what is the maximum weekly profit? (type integers or decimals rounded to two decimal places as needed.)

a food truck gyro vendor has weekly fixed costs of $515 and variable costs of $4.70 for each gyro combo prepared. complete parts a through c below.\n\na. let x represent the number of gyro combos prepared and sold each week. write the weekly cost function, c, for the food truck vendor. (hint: the cost function is the sum of fixed and variable costs.)\nc(x)=515 + 4.7x (use integers or decimals for any numbers in the expression.)\n\nb. the function r(x)= - 0.001x²+8.15x describes the money, in dollars, that the food truck vendor takes in each week from the sale of x gyro combos. use this revenue function and the cost function from part (a) to write the vendors weekly profit function, p. (hint: the profit is the difference between the revenue and the cost functions.)\np(x)= - 0.001x²+8.15x-(515 + 4.7x)= - 0.001x²+3.45x - 515 (simplify your answer. use integers or decimals for any numbers in the expression.)\n\nc. use the vendors profit function to determine the number of gyro combos that should be prepared and sold each week to maximize profit. what is the maximum weekly profit? (type integers or decimals rounded to two decimal places as needed.)

Answer

Explanation:

Step1: Recall cost - revenue - profit relationship

Profit $P(x)=R(x)-C(x)$. Given $C(x)=515 + 4.7x$ and $R(x)= - 0.001x^{2}+8.15x$.

Step2: Calculate the profit function

$P(x)=(-0.001x^{2}+8.15x)-(515 + 4.7x)=-0.001x^{2}+8.15x - 515-4.7x=-0.001x^{2}+3.45x - 515$.

Step3: Find the vertex of the quadratic function

For a quadratic function $y = ax^{2}+bx + c$ ($a=-0.001$, $b = 3.45$, $c=-515$), the $x$ - coordinate of the vertex is $x=-\frac{b}{2a}$. $x=-\frac{3.45}{2\times(-0.001)}=\frac{3.45}{0.002}=1725$.

Step4: Calculate the maximum profit

Substitute $x = 1725$ into the profit function $P(x)=-0.001x^{2}+3.45x - 515$. $P(1725)=-0.001\times(1725)^{2}+3.45\times1725 - 515$. $P(1725)=-0.001\times2975625+5951.25 - 515$. $P(1725)=-2975.625+5951.25 - 515$. $P(1725)=2460.625\approx2460.63$.

Answer:

The number of gyro combos that should be prepared and sold each week to maximize profit is $1725$. The maximum weekly profit is $$2460.63$.