The Wod Chemical Company produces a chemical compound that is used as a lawn fertilizer. The compound can be produced at a rate of 10,000 pounds per day. Annual demand for the compound is 0.6 million pounds per year. The fixed cost of setting up for a production run of the chemical is $1,500, and the variable cost of production is $3.50 per pound. The company uses an interest rate of 22 percent to account for the cost of capital, and the costs of storage and handling of the chemical amount to 12 percent of the value. Assume that there are 250 working days in a year. A. What is the optimal size of the production run for this particular compound?
B. What proportion of each production cycle consists of uptime and what proportion consists of downtime?
C. What is the average annual cost of holding and setup attributed to this item? If the compound sells for $3.90 per pound, what is the annual profit the company is realizing from this item?

A. What is the optimal size of the production run for this particular compound?

first we have to determine the holding cost per unit = h = (22% + 012%) x ($3.5) = $1.19 per unit, per year

then we have to calculate the modified holding cost per year = h' = h x [1 / (D/P)] = $1.19 x [1 / (600,000/2,500,000)] = $0.9044 per unit, per year

now we have to substitute h for h' in the EOQ formula:

Q' = √ [(2 x S x D) / h'] = √ [(2 x $1,500 x 600,000) / $0.9044] = 44,612.44 ≈ 44,612 units

B. What proportion of each production cycle consists of uptime and what proportion consists of downtime?

Time between production runs = Q' / D = 44,612 / 600,000 = 0.07435333

Uptime = Q' / P = 44,612 / 2,500,000 = 0.0178448

Downtime = total time - uptime = 0.07435333 - 0.0178448 = 0.05650853

uptime = 0.0178448 / 0.07435333 = 24% of total time

downtime = 0.05650853 / 0.07435333 = 76% of total time

C. What is the average annual cost of holding and setup attributed to this item? If the compound sells for $3.90 per pound, what is the annual profit the company is realizing from this item?

average annual holding cost and setup costs = (AD/Q') + (h'Q'/2) = [($1,500 x 600,000) / 44,612] + [($0.9044 x 44,612) / 2] = $40,144

profit per unit = $3.90 - $3.50 = $0.40 per pound

total annual profit = ($0.40 x 600,000) - $40,144 = $199,856

sound is invisible, but sometimes we can feel it. when a kettle-drum is thumped with a stick that time the tight drum skin moving up and down very quickly for some time and then it pumped sound waves into the air. loudspeakers also work in a similar manner.

components of a speaker:

electromagnet

in order to translate an electrical signal into an audible sound, an electromagnet is used in looudspeakers

  suspension

suspension is used to   center the voice coil in the gap of the magnet and it exerts a restoring force to keep it there. suspension is used to limits the maximum mechanical excursion of the diaphragm and voice coil.

voice coil

voice coil is a coil of wire which is attached to the apex of a loudspeaker cone. it provides the motive force to the cone by the reaction of a magnetic field to the current passing through it.

cone

in a   loudspeaker, a   thin, semi-rigid membrane attached to the voice coil, which moves in a magnetic gap due to which it vibrates   and produced sound. it is known as diaphragm and it can also be called a cone, though not all speaker diaphragms are cone-shaped.

surround

surround is also known as front suspension. surround is used to join the cone to the chassis. together with the suspension it controls the cone excursion, and it is also used to   determine how energy which is   travelling through the cone is absorbed, and how the speaker limits when it reaches the ends of its travel.

dustcap

dustcap is used to protect the voice coil from dust and dirt. it is a part of the cone.

how speaker work

the outer part of the cone is fastened to the outer part of the loudspeaker's circular metal rim. the inner part is fixed to   voice coil that sits just in front of a permanent magnet . when loudspeaker is hooked up to a stereo, electrical signals feed through the speaker cables into the coil. it will convert the coil into an electromagnet magnet . when electricity flows back and forth in the cables, the electromagnet either repels or attract the permanent magnet. this moves the coil back and forth, and it pull and push the loudspeaker cone. like a drum skin vibrating back and forth, the moving cone pumps sounds out into the air.in this way loudspeakers works.

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