Question

Radovilsky Manufacturing Company, in Hayward, California, makes flashing lights for toys. The company operates its production facility 300 days per year. It has orders for about 12,500 flashing lights per year and has the capability of producing 105 per day. Setting up the light production cast $49. The cost of each light is $0.95. The holding cost is $0.15 per light per year. What is the optimal size of the production run? What is the average holding cost per year? What is the average setup cost per year? What is the total cost per year, including the cost of the lights?

Answer 1

Answer:

Given,

Annual demand, D = 12500,

Setting up cost, S = $ 49,

Production rate per year, P =  production facility × capability of production = 300 × 105 = 31500,

Holding cost per year, H = $ 0.15,

Hence,

(i) Optimal size of the production run,

$Q = \sqrt{\frac{2DS}{H(1-\frac{D}{P})}}=\sqrt{\frac{2\times 12500\times 49}{0.15(1-\frac{12500}{31500})}}=3679.60238126\approx 3680$

(ii) Average holding cost per year,

$=\frac{QH}{2}(1-\frac{D}{P})$

$=\frac{3680\times 0.15}{2}(1-\frac{12500}{31500})$

$=166.476190476$

$\approx \ 166.48$

(iii) Average setup cost per year,

$=\frac{D}{Q}\times S$

$=\frac{12500}{3680}\times 49$

$=166.44021739$

$\approx \ 166.44$

(iv) Total cost per year = average setup cost per year + average holding cost per year + cost to purchase 12500 lights

= 166.44 + 166.48 + 12500(0.95)

= $ 12207.92

Answer 2

The correct answers are:

(i) Optimal size of the production run= 3,680,

(ii) Average holding cost per year = $166.44,

(iii) Average setup cost per year = %116.44, and

(iv) Total cost per year =$12,207.92

What is the cost?

In terms of accounting, cost refers to the amount of cash or the cash equivalent which is provided up for an asset. It considers all costs, which is essential to get an asset in place and ready for use.

Computation of the above cases:

According to the given information,

Annual demand(D) = 12,500,

Setting up cost(S) = $49,

Production rate per yea(P):

$\text{P}=\text{Production Facility} \times\text{Capability of Production}\\\\\text{P}= 300\times 105\\\\\text{P}= 31500,$

Holding cost per year(H) = $0.15

(i). Optimal size of the production run(o):

$\text{Q}= \sqrt{\dfrac{2DS}{H(1-\dfrac{D}{P} )} }\\\\\\\text{Q}= \sqrt{\dfrac{2\times15,500\times49}{0.15(1-\dfrac{12,500}{31,500} )} }\\\\\\\text{Q}=3679.6023$

(ii). Average holding cost per year(HC):

$\text{HC}=\dfrac{\text{QH}}{2}(1-\dfrac{D}{P})\\\\\\\text{HC}=\dfrac{3,680 \times 0.15}{2}(1-\dfrac{12,500}{31,500})\\\\\text{HC}=166.4761$

(iii). Average setup cost per year(SC):

$\rm{SC}=\frac{\rm{D}}{\rm{Q}}\times\rm{S}\\\\\rm{SC}=\dfrac{12,500}{3,680}\times 49\\\\\rm{SC}=\ 166.44$

(iv) Total cost per year(TC):

$= \text{Average Setup Cost Per Year + average holding cost per year + cost to purchase 12500 lights}= 166.44 + 166.48 + 12500(0.95)= 12207.92$

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