Fundamental of modern manufacturing 5th edition Chapter 1 Pr

Fundamental of modern manufacturing 5th edition Chapter 1 Problem Question 1.5:

A plastic molding machine produces a product whose annual demand is in the millions.
The machine is automated and used full time just for the production of this product. The
molding cycle time = 45 sec. No tooling is required other than the mold, which cost
$100,000 and is expected to produce 1,000,000 moldings (products). The plastic molding
compound costs $1.20/lb. Each molding weighs 0.88 lb. The only labor required is for a
worker to periodically retrieve the moldings. Labor rate of the worker = $18.00/hr
including overhead. However, the worker also tends other machines and only spends 20%
of his time on this machine. Setup can be ignored because of the long production run. The
molding machine was purchased for $500,000 installed, its anticipated life = 10 years,
and it operates 6000 hours per year. Equipment overhead rate = 30%. Assume availability
= 100% and scrap rate = 0. Determine (a) the hourly production rate of the machine, (b)
annual quantity of product molded, and (c) cost per piece.

Please give a clear explanation of what cost per piece should be.

Solution

(a) With a cycle time T_c = 45 sec = 0.75 min, R_p = 60/0.75 = 80 pc/hr. Factoring in the 98% proportion uptime, R_p = 0.98(80) = 78.4 pc/hr

Annual quantity of product = 6000(78.4) = 470,400 pc/yr

(b) Equipment cost rate C_eq = 500,000(1.30)/(60 x 10 x 6000) = $0.1806/min.

Mold cost per piece C_t = 100,000/1,000,000 = $0.10/pc

Labor cost rate C_L = 18.00(0.20) = $3.60/hr = $0.06/min

Finally, cost per piece C_pc = 1.20(0.88) + (0.06 + 0.1806)(0.75) + 0.10 = $1.34/pc