A manufacturer sells lamps at six dollars each and sells 3000 each month. For each one dollar that the price is increased, 1000 fewer lamps are sold each month. It costs 4 dollars to make one lamp. What price should lamps be sold at to maximize profit

Price it will be sold to make maximum profit = $6.5 each

Explanation:

The challenge is to maximize profit.

We can assign to be the number of dollars obtained per unit price per flashlight.

Recall:

Profit = Revenue - Cost

Revenue = price charged x number sold =

Cost = cost to produce a unit x number of units produced

Profit =

At the point of maximum profit, the change in profit with respect to price will be = 0. In mathematical terms, the derivative of the profit will be = zero

∴

from this, we can see that at maximum profit, x = 0.5

∴ Price it will be sold to make maximum profit = $6.00 + 0.5 = $6.5 each

among other factors, composers started writing dynamic markings in their scores because "new instruments allowed for more dynamic ranges and contrast."

dynamics allude to the loudness or softness of music. dynamics offer an approach to demonstrate articulation in sheet music. they to drive the enthusiastic substance of music through volume and force. maybe you could alter both the volume and the shading profundity on your screen at the same time. we can likewise think about the force side of elements as the quality of a note. a few notes are intended to be played delicately and gently, while others are intended to be played all the more firmly.  

some dynamics markings have a letter 'm,' which remains for mezzo, signifying 'medium.' so a mezzo piano unique stamping resembles this (mp) and intends to play medium calm, while a mezzo specialty dynamic resembles this (mf) and intends to play medium loud.