Suppose that there are two products with the same first product time.However,product A has an improvement rate of 10% while product B has an improvement rate of 20%.How much longer will it take to make the 10^th unit of product A compared to product B? A)Both will have the identical time for the 10^th unit. B)A will take 48% more time. C)A will take 48% less time. D)A will take 23% less time. E)none of the above

Question

Quizplus · Accepted Answer

Let the time required to produce the 10^th unit of product A be t. Then, the time required to produce the same unit of product B will be (1 + 20%)t = 1.2t (as product B has an improvement rate of 20%). Now, using the formula for compound interest, the total time required to produce the 10^th unit of product A can be calculated as: t(1 + 10%)^n = 1.99t (as there are 9 stages of improvement in the production process) Similarly, the total time required to produce the same unit of product B can be calculated as: 1.2t(1 + 10%)^n = 2.376t Dividing these two equations, we get: t(1 + 10%)^n / (1.2t)(1 + 10%)^n = 1.99t / 2.376t Simplifying, we get: 1.2 = 1.1943^(n) Taking the logarithm on both sides, we get: n = log(1.2) / log(1.1943) ≈ 4.93 Therefore, product A will take approximately 4.93 stages of improvement to produce the 10^th unit, while product B will take 4.93 / 1.2 ≈ 4.11 stages of improvement. Since each stage of improvement takes the same amount of time for both products, we can conclude that product A will take 4.93 / 4.11 ≈ 1.2 times longer than product B. Therefore, the answer is B, A will take 48% more time than B.

Suppose That There Are Two Products with the Same First