The daily profit, 𝑃 (in $), of an oil refinery is given by 𝑃(𝑥) = −0.04𝑥2 + 10𝑥 where x isthe number of barrels of oil refined.a. How many barrels will give maximum profit and what is the maximum profit?

An barrels manufacturer can produce up to 300 barrels per day. The profit made fromthe sale of these barrels can be modelled by the function P (x) = − 10x2 + 3500x −66000 where P(x) is the profit in rupees and x is the number of barrels made and sold.(i) When no barrels are produce what is a profit /loss?(ii) What is the break even point ? (Zero profit point is called break even)(iii) What is the profit/loss if 175 barrels are produced(iv) What is the profit/loss if 400 barrels are produced

A firm’s price in a perfectly competitive market is 1000. Its cost function is 32 C(x) = 0.01x 3x− 11+08x 96+0 , where x ≥ 0 is the number of units produced and sold. (a) Find an expression for the profit function π(x) for x ≥ 0. (b) Find all stationary points and determine the profit maximising level of output. answer to six decimal places. 1 √1−𝑥𝑥 . State your answer using (c) Using a sign diagram, determine the intervals over which π(x) is increasing and decreasing. (d) Determine the intervals over which π(x) is concave and convex. (e) Where is the point of inflection in C(x)? Give an economic interpretation of the point of inflection.

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

5 The diagram shows the market for refined oil with equilibrium of X.What will be the new equilibrium when a major oil refinery shuts down for repair work?1 point

A shopkeeper mixed low-quality vegetable oil costing Rs. 40 per litre with sunflower refined oil costing Rs. 80 per litre in the ratio of 2 ∶ 3 respectively. If he sold the mixture at Rs. 100 per litre, find his profit percentage.42.75%47.50%51.50%56.25%None