Question

Up, Up, and Away is a producer of kites and wind socks. Relevant data on the bottleneck operation in the shop for th upcoming fiscal year are given in the following table: 1

L ⋮ ⋮ The shop works two shifts per day, 8 hours per shift, 180 days per year. Currently, the company operates four machines, and desires a 25 percent capacity cushion. How many machines should be purchased to meet the upcoming year's demand without resorting to any short-term capacity solutions? The number of additional machines required is (Enter your response rounded up to the next whole number.)

Answer 1

To find how many additional machines are needed, calculate the total annual capacity, add a 25 percent cushion, then divide by the production per machine to find the total number of machines required. Subtract the current number of machines to get the additional machines needed, rounded up to a whole number.

Step-by-step explanation:

To determine how many machines should be purchased by Up, Up, and Away, a kite and wind sock producer, to meet the upcoming year's demand without resorting to short-term capacity solutions, we need to calculate the required capacity including the desired 25 percent capacity cushion. The shop operates two shifts per day at 8 hours per shift for 180 days a year. Assuming the maximum capacity is reached with the current four machines, we first calculate the total capacity with these conditions and then, we add the 25 percent cushion to determine the ideal total capacity. Finally, we ascertain the number of additional machines needed to meet this ideal capacity.

For example, if the full capacity without a cushion is 100 units, with a 25 percent cushion, the shop would aim for a capacity of 125 units. If each machine can produce 25 units, the company currently uses four machines to meet the initial 100 units. To meet the new goal of 125 units, however, the company would need five machines in total (since 125÷ 25 = 5), implying that one additional machine is required.

The number of additional machines required will be calculated based on similar logic specific to the actual production capabilities of the machines and the determined ideal capacity with the cushion.

Answer 2

To calculate the number of machines Up, Up, and Away needs to purchase, one must determine the full existing capacity, adjust for the desired capacity cushion by multiplying by 1.25, and divide by the capacity of an individual machine. Subtract the number of current machines to find the number of additional machines required, and round up to the nearest whole number.

Step-by-step explanation:

To determine how many additional machines should be purchased by Up, Up, and Away to meet the upcoming year's demand and maintain a 25 percent capacity cushion, we need to calculate the required capacity based on given operational time and then account for the cushion. Unfortunately, the question does not provide specific details on the current capacity or the demand in numbers. However, if we assume that the existing four machines are running at full capacity, we need to ensure that the total capacity includes a cushion. This can be calculated by multiplying the full capacity by 1.25 (to account for the 25% cushion).

To do this:

1. Determine the full capacity by multiplying the number of shifts, hours per shift, and days per year.
2. Multiply full capacity by 1.25 to incorporate the capacity cushion.
3. Divide the required capacity with cushion by the individual machine capacity to find the total number of machines needed.
4. Subtract the current number of machines (four) from the total number needed to determine the number of additional machines required.

Since we cannot provide a numerical answer due to the lack of information on current capacity or demand, we advise the student to follow the steps with the actual numbers to get the solution. Remember to round up to the nearest whole number because you cannot have a fraction of a machine.