A cereal company estimates that its monthly cost is 𝐶(𝑥)=400𝑥2+300𝑥C(x)=400x 2 +300x and its monthly revenue is 𝑅(𝑥)=−0.6𝑥3+900𝑥2−400𝑥+700R(x)=−0.6x 3 +900x 2 −400x+700, where x is in thousands of boxes sold. The profit is the difference between the revenue and the cost.What is the profit function, P(x)?A.𝑃(𝑥)=0.6𝑥3−500𝑥2+700𝑥−700P(x)=0.6x 3 −500x 2 +700x−700B.𝑃(𝑥)=0.6𝑥3−1300𝑥2+100𝑥+700P(x)=0.6x 3 −1300x 2 +100x+700C.𝑃(𝑥)=−0.6𝑥3+1300𝑥2−100𝑥+700P(x)=−0.6x 3 +1300x 2 −100x+700D.𝑃(𝑥)=−0.6𝑥3+500𝑥2−700𝑥+700P(x)=−0.6x 3 +500x 2 −700x+700SUBMITarrow_backPREVIOUS

Suppose a granola bar company estimates that its monthly cost is 𝐶(𝑥)=500𝑥2+400𝑥C(x)=500x 2 +400x and its monthly revenue is 𝑅(𝑥)=−0.6𝑥3+800𝑥2−300𝑥+600R(x)=−0.6x 3 +800x 2 −300x+600, where x is in thousands of granola bars sold. The profit is the difference between the revenue and the cost.What is the profit function, P(x)?A.𝑃(𝑥)=−0.6𝑥3+1300𝑥2+100𝑥+600P(x)=−0.6x 3 +1300x 2 +100x+600B.𝑃(𝑥)=0.6𝑥3+300𝑥2−700𝑥+600P(x)=0.6x 3 +300x 2 −700x+600C.𝑃(𝑥)=−0.6𝑥3+300𝑥2−700𝑥+600P(x)=−0.6x 3 +300x 2 −700x+600D.𝑃(𝑥)=0.6𝑥3−300𝑥2+700𝑥−600P(x)=0.6x 3 −300x 2 +700x−600SUBMITarrow_backPREVIOUS

Determine the total profit function, P(x)

The organizer of a sports event estimates that if the event is announced 𝑥 days in advance, the revenueobtained will be 𝑅(𝑥) thousand dollars, where𝑅(𝑥) = 400 + 120𝑥 − 𝑥2The cost of advertising the event for 𝑥 days is 𝐶(𝑥) = 2𝑥2 + 300a. Find the profit function 𝑃(𝑥) = 𝑅(𝑥) − 𝐶(𝑥) and sketch its graph.b. How many days in advance should the event be announced in order to maximize profit? What is themaximum profit?c. What is the ratio of revenue to cost 𝑄(𝑥) = 𝑅(𝑥)𝐶(𝑥) at the optimal announcement time found in part (b)?What happens to this ratio as 𝑥 → 0? Interpret these results

The cost for a company to produce x smartphones can be modeled by C(𝑥)=2𝑥+35C(x)=2x+35 and the company's total profit after selling x smartphones can be modeled by P(x) = -x2 + 120x - 435. Which function represents the company's revenue for selling smartphones? (Recall that profit equals revenue minus cost.)A.R(𝑥)=−𝑥2+118𝑥−470R(x)=−x 2 +118x−470B.R(𝑥)=−𝑥2+122𝑥+400R(x)=−x 2 +122x+400C.R(𝑥)=−𝑥2+122𝑥−470R(x)=−x 2 +122x−470D.R(𝑥)=−𝑥2+122𝑥−400R(x)=−x 2 +122x−400SUBMITarrow_backPREVIOUS

The total cost (in dollars) for a company to manufacture and sell 𝑥 items per week is 𝐶=50⁢𝑥+2960, whereas the revenue brought in by selling all 𝑥 items is 𝑅=140⁢𝑥-0.6⁢𝑥2. How many items must be sold to obtain a weekly profit of $400?Hint: Profit = Revenue - Cost.They need to sell or items.