Calculus Answers

Direction: solve each word problem involving optimization. Make a sketch of your work if

necessary, and then apply differentiation.

6. A business sells 2000 units of a product per month at a price of Php500 each. It

can sell 250 more items per month for each Php12.50 price reduction. What price

per unit will maximize the monthly revenue?

7. A paper is thrown upward from height of 10 feet, initially at 5 feet per second. What

is the maximum height of the paper?

PLEASE ANSWER MY QUESTION QUICKLY !!!

DEADLINE : 04/29/2022 11 : 00 PM

Direction: solve each word problem involving optimization. Make a sketch of your work if

necessary, and then apply differentiation.

3. A two-pen corral is to be built. The outline of the corral forms two identical adjoining

rectangular regions. There is 90 feet of fencing available. Find the maximum

enclosed area and the dimensions of the corresponding enclosure.

4. The product of two positive integers is 240. What is the smallest possible sum for

the two numbers?

5. A manufacturing company has determined that the cost (in pesos) of producing

x units of a product is modelled by the function f(x) = 0.0001x^2 − 0.02x + 400.

How many units of the product will minimize production cost?

Direction: solve each word problem involving optimization. Make a sketch of your work if

necessary, and then apply differentiation.

1. A three-sided fence is to be built next to a straight section of a river, which forms

the fourth side of the rectangular region. The enclosed area is equal to 1800 square

feet. Find the maximum perimeter and the dimension of the corresponding

enclosure.

2. A box with no top will be built by taking a 12 inch × 16 inch sheet of cardboard

and cutting it into x number of pieces (in square inches) out of each corner and

folding up the sides. Find the value of x that maximize the volume of the box.

PLEASE ANSWER MY QUESTION QUICKLY !!!

DEADLINE : 04/29/2022 11 : 00 PM

Water is being poured at the rate of 3pi m^3 /min. into an inverted conical tank that

is 10-meter deep with a radius of 6 meters at the top. If the water level is rising at the

rate of 1/5 m/min and there is a leak at the bottom of the tank, how fast is the water

leaking when the water is 6-meter deep? V = Vin –Vout

The temperature of piston head in a combustion engine during the worming up period can be modelled by equation (6): ----------------------------------------------- 𝑇=𝐾𝑇𝑜(𝐿+𝑡2𝑐𝑜𝑠𝑡3) ------------------------------------------------------------------------------------------------------------ Where T is the piston head instant temperature in Kelvin, K and L are constants for a given engine, t is time in second, and T be the environment temperature in Kelvin. ------------------------------------------------------------------------------------------------------------ Considering the following parameters for the given engine including 𝐾=3, 𝐿=3.4×10−3𝑠2and To=295 K. --------------------------------------------------------------------------------------------------------------- a) Calculate the mean temperature for piston head between t=0 and t=2 s. ------------------------------------------------------------------------- b) A numerical integration technique (n=8 intervals) to find the mean over a range of0≤𝑥≤𝜋.