(a) The optimal machine assignment time is 7 minutes. (b) The duration of a complete cycle is 25 minutes. There will indeed be 7 minutes of idle time for the operator. (c) If an operator is assigned three machines, the cost per unit produced amounts to $13.88 per unit. To elaborate, loading takes 3 minutes, unloading lasts 2 minutes, while the runtime is 20 minutes. The time spent on inspection and packing takes 1 minute. The operator's wage is $10 per hour, and machine cost is $30 per hour. Ideal machine assignment can be calculated via machine cycle time divided by the operator time per machine. The machine cycle includes run, load, and unload time, which sums to 25 minutes. The time contribution per machine is 6 minutes, resulting in an ideal machine assignment of 25 ÷ 6 = 4.17, indicating the assignment of four machines to an operator is suboptimal, leading to idle time. The complete cycle takes 25 minutes. Idle operator time is calculated as cycle time minus the operational contributions of the machines assigned, culminating in 7 minutes of idle time. The total cost of each unit produced comes from combining operator costs with machine costs, multiplied by cycle time adjusted for hours, resulting in $13.88 per unit.
The total value of the inventory lost in the tornado is $105,700. Explanation: The relationship is captured in this equation: Beginning inventory + inventory purchases + Gross profit = Sales + ending inventory. Plugging in the figures, $228,350 + $199,400 + $322,050 = $644,100 + ending inventory resolves to $749,800 = $644,100 + ending inventory. Thus, determining that the ending inventory amounts to $749,800 - $644,100 results in $105,700. The gross profit is calculated as Gross profit percentage multiplied by sales: 50% multiplied by $644,100 yields $322,050. Since the inventory was destroyed in the tornado, we assume the ending inventory lost corresponds to $105,700.
