Question

Suppose a manufacturer produces three models of air-conditioner unit: deluxe, standard, and economy. The deluxe model can be assembled in four hours, the standard in three hour, and the economy in two hours. The assembly line has 800 staff hours available each week.

(a) If the demands for deluxe, standard, and economy are in the ratio 2:3:4, calculate

(i) the total time needed to assemble (2+3+4) 9 units, and

(ii) the total number of units produced per week.

(b) If the demand ratio changes to 3:3:3, recalculate

(i) the total time needed to assemble (3+3+3) 9 units, and

(ii) the total number of units produced per week.

Answer 1

Deluxe model time (Dt) = 4 hours

Standard model time (St) = 3 hours

Economy model time (Et) = 2 hours

Total time available (T) = 800 hours

a)

1) Time for 9 units:

Number of Deluxe = 2

Number of Standard = 3

Number of Economy = 4

Time for 9 units = Number of Deluxe*Dt + Number of Standard*St + Number of Economy*Et = 2*4 + 3*3 + 4*2 = 25 hours

2) Total number of units produced per week:

25 hours are required for 9 units

Unit produced per hour = 9/25

Number of units in 800 hours = 800/25*9 = 288

b)

1) Time for 9 units:

Number of Deluxe = 3

Number of Standard = 3

Number of Economy = 3

Time for 9 units = Number of Deluxe*Dt + Number of Standard*St + Number of Economy*Et = 3*4 + 3*3 + 3*2 = 27 hours

2) Total number of units produced per week:

27 hours are required for 9 units

Unit produced per hour = 9/27

Number of units in 800 hours = 800/27*9 = 266 (Round down)