(1 point The revenue from selling $$ q $$ items is $$ R(q)=625 q-q^{2} $$, and the total coat is $$ C(q)=100+11 q $$. Write a function that gives the total proft earned, and find the quartily which maximizes the profi. Profit $$ x(q)= $$ Quantiry maximizing profti $$ q= $$

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We first find the profit function by subtracting the cost function from the revenue function:
$$
x(q)=R(q)-C(q)=\left(625q-q^2\right)-\left(100+11q\right)
$$
Simplify the expression:
$$
x(q)=-q^2+625q-11q-100=-q^2+614q-100
$$

To maximize this quadratic function, we find the vertex. For a quadratic of the form 
$$
f(q)=aq^2+bq+c
$$
with $$a<0$$ (ensuring a maximum), the optimal $$q$$ is given by:
$$
q=-\frac{b}{2a}
$$

In our case, $$a=-1$$ and $$b=614$$:
$$
q=-\frac{614}{2(-1)}=\frac{614}{2}=307
$$

Thus, the profit function is:
$$
x(q)=-q^2+614q-100
$$
and the quantity that maximizes the profit is:
$$
q=307
$$
Profit function: $$ x(q) = -q^2 + 614q - 100 $$ Quantity that maximizes profit: $$ q = 307 $$

(1 point The revenue from selling items is , and the total coat is . Write a function that gives the total proft earned, and find the quartily
which maximizes the profi.
Profit
Quantiry maximizing profti

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(1 point The revenue from selling items is , and the total coat is . Write a function that gives the total proft earned, and find the quartily which maximizes the profi. Profit Quantiry maximizing profti