Suppose that the price per unit in dollars of a cell phone production is modeled by p= $45 -0.0125x, where x is in thousands of phones produced, and the revenue represented by
thousands of dollars is R X .p. Find the production level that will maximize revenue.

The production level that will maximize the revenue is 1800 (in thousands of phones produced), that is, production of 1,800,000 phones will maximize the revenue.

Step-by-step explanation:

The price per unit of phone is given as

p = 45 - 0.0125x

where x is in thousands of phones produced

Revenue = (price per unit) × (number of units)

Revenue = (45 - 0.0125x) × x

= (45x - 0.0125x²)

To find the maximum revenue, we need to obtain the maximum value of the revenue function.

R(x) = (45x - 0.0125x²)

At maximum point, (dR/dx) = 0 and (d²R/dx²) < 0

R(x) = (45x - 0.0125x²)

(dR/dx) = 45 - 0.025x

at maximum point, (dR/dx) = 0

(dR/dx) = 45 - 0.025x = 0

0.025x = 45

x = (45/0.025) = 1800

Hence, the production level that will maximize the revenue is 1800 (in thousands of phones produced)

That maximum revenue is thus

R(x) = (45x - 0.0125x²)

R(1800) = (45×1800) - (0.0125×1800²)

= 40,500

Hope this Helps!!!

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).