Two product (X and Y) are produced on two machines (A and B). It is required tha

Question

Two product (X and Y) are produced on two machines (A and B). It is required that 10units/day of product X be produced on machine A and 12units/day of product X be produced on machine B; it is required that 20units/day of product Y be produced on machine A. Production times per unit are Tax = 1 hour, Tbx = 2 hours, and Tay = 1.6 hours. During a day, 8 hours are available or production. Machine A is efficiently utilized 80% of the time; machine B is efficiently utilized 70% of the time.

(a) Determine the number of machines of type A and B that should be provided each day.

(b) If SD[PXA] = 2, SD[PYA] = 3.4, SD[PXB] = 2.2, determine the standard deviation for the number of machines of each type required.

(c) If SD[Tij] denotes the standard deviation of production time/unit for product i on machine j and SD[TXA] = 0.1, SD[TYA] = 0.2, SD[TXB ] = 0.15, determine the standard deviation for the number of machines of each type

(d) Combine the standard deviation data for parts (b) and (c) to determine the standard deviation for the number of machines of each type required.

Explanation / Answer

Given that ---------   

Number of product X be produced on machine A = 10 Units/day

Number of product X be produced on machine B = 12 Units/day

Number of product Y be produced on machine A = 20 Units/day

Number of hours available per day = 8 Hours

But according to given time utilizing efficiency ----

Number of hours available for A = 80*8/100 = 6.4 hours ______ (1)

Number of hours available for B = 70*8/100 = 5.6 hours ______ (2)

Tax = 1 hour

So, For X on Machine A, required work hours per day = 10*1 = 10

Tay = 1.6 hours

So, For Y on Machine A, required work hours per day = 20*(1.6) = 32

Tbx = 2 hours

So, For X on Machine B, required work hours per day = 12*2 = 24

So, For Machine A total required work hours per day = 32+10 = 42 _____ (3)

and For Machine B total required work hours per day = 24 ________ (4)

(a) from (1) and (3) ----

Number of machines of type A = 42/6.4 = 6.5625

Means at least 7 machines of type A are needed.

from (2) and (4) ------

Number of machines of type B = 24/5.6 = 4.2857

Means at least 5 machines of type B are required.

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