a manufacturing company produces two types of sprocketsa and

a manufacturing company produces two types of sprockets,a and b.for each $1.00 spent on the production of sprocket a,the company spends $0.45 on materials,$0.25 on labor and $o.15 on overhead.for each $1.00 spent in the production of sprockets B,the company spends $0.0 on materials,$0.20 on labour and $0.10 on overhead.

let a=[0.45 0.25 0.15] and b=[0.40 0.20 0.10] represnt this information.and let x1 represent the total amount in dollers which was spent on sprocket A during a certain production cycle,while X2 represent the corresponding amount spend on sprocket B.at the end of the production run the books indicated a total cost of $260for materials,$140 for labour and $80 on overhead.use this information to determine the values of x1 and x2.be sure to check your answer.

Solution

There seems to be something missing. The amounts 0.45, 0.25 and 0.15 do not add uptto 1. Similarly , the amounts 0.40, 0.20 and 0.10 do not add upto 1. If we treat the missing amounts of 0.15 as miscellaneous expenditure in case of sprocket a and 0.30 as miscellaneous expenditure in case of sprocket b, even then the amount of aggregate miscellaneous expenditure has not been furnished. In absence of this information, we cannot proceed further.

NOTE:

The problem can be solved as under if the complete information is available:

The total amount spent on the production of the sprockets a and b is $ 260+ 140 +80 = $480. Therefore, x₁+ x₂ = 480…(1) Further, since x₁ was spent on sprocket a, and x₂ was spent on sprocket b, we have [ 0.45x₁ 0.25x₁ 0.15x₁ ] as the break-up of expenditure on the sprocket a and [0.40x₂ 0.20x₂ 0.10x₂] as the break-up of expenditure on the sprocket b. Then the expenditure on materials is 0.45x₁ + 0.40x₂, the expenditure on labor is 0.25x₁ + 0.20x₂ and the expenditure towards the overheads is 0.15x₁ + 0.10x₂. Therefore, we have the following equations:

0.45x₁ + 0.40x₂ = 260 or, 45x₁ + 40x₂ = 26000 or, 9x₁ + 8x₂ = 5200….(2)

0.25x₁ + 0.20x₂ = 140 or, 25x₁ + 20x₂ = 14000 or, 5x₁ + 4x₂ = 2800…(3) and

0.15x₁ + 0.10x₂ = 80 or, 15x₁ + 10x₂= 8000 or, 3x₁ + 2x₂ = 1600…(4)

On multiplying both the sides of the 1^st equation by 8, we get 8x₁ + 8x₂ = 3840….(5) Now, on subtracting the 5th equation from the 2^nd equation, we get 9x₁ + 8x₂ - 8x₁ - 8x₂ = 5200- 3840 or, x₁ = 1360.

This cannot be correct, as x₁+ x₂ = 480 so that x₂ would be negative. This is not possible.