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 11,800 flashing lights per year and has the capability of producing 95 per day. Setting up the light production costs $48. The cost of each light is $0.95. The holding cost is $0.10 per light per year. A) What is the optimal sizeof the production run?
B) What is the average holding cost per year?
C) What is the average setup cot per year?
D) What is the total cost per year, including the cost of the lights?

Please see answers below.

Explanation:

Annual demand rep D=11,800

Setting up cost rep S = $48

Holding cost per year rep H=$0.1

Production rate per year = Production facility × Capability of production

=300 × 95

=28,500

Therefore;

a. Optimal size of the production

Q = √2DS/H(1-D/P)

= √2×11,800×48/0.1(1-11,800/28,500)

=√11328000-0.5859649123

=√11328000.586

=$3,366

b. Average holding cost per year

=QH/2(1-D/P)

=3,366×0.1/2(1-3,366/28,500)

=168.3(0.8818947368)

=$148.42

C. Average set up cost

=D/Q × S

=11,800/3,366 × 48

=$168.27

D. Total cost per year = Average set up cost + Average holding cost per year + Cost to purchase 11,800 lights

= $148.42 + $168.27 + 11,800(0.95)

= $11,526.69

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