The demand function of a product for a manufacturer is 𝑝 (𝑥) = 𝑎𝑥 + 𝑏. The manufacturer knows that he can sell 1250 units when the price is GHS5 per unit and he can sell 1500 units at a price of GHS4 per unit. Find the total, and average revenue functions.

For a certain product, the demand function is 𝐷(𝑄) = 1000 − 25𝑄 and thesupply function is 𝑆(𝑄) = 100 + 𝑄2. Calculate:a) The market equilibrium price and quantityb) Compute the consumer and producer surplus.

A manufacturer determines that m employees will produce a total of q units each week. The relation between the number of employees and the quantity is given as: 𝑞 = 5𝑚2 + 2𝑚 + 4. Given that the demand function for the product is given as 𝑝 = 1000 𝑞+8 , determine a. The rate of change of price with respect to quantity b. The rate of change of price with respect to the number of employees c. Determine the marginal revenue when the number of employees is 15

The demand function Q and cost function C(Q) of a commodity are given by the equations \[Q=20-0.01P,\] and C(Q)=60+6Q, where P and Q are the price and quantity, respectively. The total revenue function (TR) in terms of P is

The demand function of a good is given byP = 140 − 35Qwhere P denotes the price and Q the quantity.(a) Write down the revenue R as a function of the quantity Q.(b) Find the quantity Q that maximizes the revenue and find the maximumrevenue

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