Marshall Co. produced a pilot run of fifty units of a recently developed piston

Question

Marshall Co. produced a pilot run of fifty units of a recently developed piston used in one of its products. Marshall expected to produce and sell 1,915 units annually. The pilot run required an average of 0.55 direct labor hours per piston for 50 pistons. Marshall experienced an seventy nine percent learning curve on the direct labor hours needed to produce new pistons. Past experience indicated that learning tends to cease by the time 800 pistons are produced. Marshall's manufacturing costs for pistons are presented below. Direct labor $14.00 per direct labor hour Variable overhead $11.00 per direct labor hour Fixed overhead $20.00 per direct labor hour Materials $4.00 per unit Marshall received a quote of $8.00 per unit from Kytel Machine Co. for the additional 1,840 needed pistons. Marshall frequently subcontracts this type of work and has always been satisfied with the quality of the units produced by Kytel. If the pistons are manufactured by Marshall Co, the average direct labor hours per unit for the first 800 pistons (including the pilot run) produced is calculated to be (use five decimal places in calculating the average time): A) 0.27117 B) 0.34326 C) 0.16924 D) 0.43450 E) 0.21423 Marshall Co. produced a pilot run of fifty units of a recently developed piston used in one of its products. Marshall expected to produce and sell 1,915 units annually. The pilot run required an average of 0.55 direct labor hours per piston for 50 pistons. Marshall experienced an seventy nine percent learning curve on the direct labor hours needed to produce new pistons. Past experience indicated that learning tends to cease by the time 800 pistons are produced. Marshall's manufacturing costs for pistons are presented below. Direct labor $14.00 per direct labor hour Variable overhead $11.00 per direct labor hour Fixed overhead $20.00 per direct labor hour Materials $4.00 per unit Marshall received a quote of $8.00 per unit from Kytel Machine Co. for the additional 1,840 needed pistons. Marshall frequently subcontracts this type of work and has always been satisfied with the quality of the units produced by Kytel. If the pistons are manufactured by Marshall Co, the average direct labor hours per unit for the first 800 pistons (including the pilot run) produced is calculated to be (use five decimal places in calculating the average time): A) 0.27117 B) 0.34326 C) 0.16924 D) 0.43450 E) 0.21423

Explanation / Answer

n th unit can be calculated using the formula

The unit time (i.e., the number of direct labour hours required) for the

n th unit can be calculated using the formula

T(n)= T(1)*n^(Natural log of learning %age/ Natural log of (n-1) T(800)= 0.55*800^(log0.79/log(800-1)) Using online equation solver, T(800) 0.434481 or 0.43450 ANSWER: D- 0.43450

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