A company's production facility, consisting of two identical machines, currently caters only to product A. The annual demand for the product is 4000 units. Management has now decided to introduce another product, B, which uses the same facilities as that of product A. Product B has an annual demand of 2000 units. In view of the uncertainties involved in producing two products, management desires to have an overall 10 percent capacity cushion. Given the following additional information, how many more machines are required? (Assume 8 hours/shift, 2 shifts/day, 250 days/year, and that no overtime is allowed.) $$\begin{array} { | c | c | c | c | }
\hline \text { Product } & \begin{array} { c }
\text { Processing } \
\text { Time perUnit } \
\text { (inhours) }
\end{array} & \begin{array} { c }
\text { Setup Time } \
\text { per Batch } \
\text { (in hours) }
\end{array} & \begin{array} { c }
\text { Batch Size } \
\text { (units) }
\end{array} \
\hline A & 2.0 & 8 & 100 \
\mathrm {~B} & 2.8 & 16 & 200 \
\hline
\end{array}$$
A) One additional machine is necessary.
B) No additional machines are necessary.
C) More than two additional machines are necessary.
D) Two additional machines are necessary.

Question

A company's production facility, consisting of two identical machines, currently caters only to product A. The annual demand for the product is 4000 units. Management has now decided to introduce another product, B, which uses the same facilities as that of product A. Product B has an annual demand of 2000 units. In view of the uncertainties involved in producing two products, management desires to have an overall 10 percent capacity cushion. Given the following additional information, how many more machines are required? (Assume 8 hours/shift, 2 shifts/day, 250 days/year, and that no overtime is allowed.) $$\begin{array} { | c | c | c | c | } 
\hline \text { Product } & \begin{array} { c } 
\text { Processing } \
\text { Time perUnit } \
\text { (inhours) }
\end{array} & \begin{array} { c } 
\text { Setup Time } \
\text { per Batch } \
\text { (in hours) }
\end{array} & \begin{array} { c } 
\text { Batch Size } \
\text { (units) }
\end{array} \
\hline A & 2.0 & 8 & 100 \
\mathrm {~B} & 2.8 & 16 & 200 \
\hline
\end{array}$$
A) One additional machine is necessary.
B) No additional machines are necessary.
C) More than two additional machines are necessary.
D) Two additional machines are necessary.

Quizplus · Accepted Answer

To calculate the total machine hours required, we need to consider both the processing and setup times for both products. For product A: (4000 units / 100 units per batch) * 8 hours setup + 4000 units * 2 hours processing = 80 + 8000 = 8080 hours. For product B: (2000 units / 200 units per batch) * 16 hours setup + 2000 units * 2.8 hours processing = 160 + 5600 = 5760 hours. Total hours = 8080 + 5760 = 13840 hours. With a 10% capacity cushion, required hours = 13840 * 1.1 = 15224 hours. Available hours per machine = 8 hours/shift * 2 shifts/day * 250 days/year = 4000 hours. Machines required = 15224 / 4000 = 3.81. Since we already have 2 machines, we need 2 additional machines to meet the demand with the desired capacity cushion.

A Company's Production Facility, Consisting of Two Identical Machines, Currently