Question

Kitchen Korner produces refrigerators, dishwashers, and stoves at three different factories. The table gives the number of each product produced at each factory per day. Kitchen Korner receives an order for 110 refrigerators, 150 dishwashers and 114 ovens. How many days should each plant be scheduled to fill this order? ANSWER: 6 days for factory A, 2 days for factory B, and 3 days for Factory C

Appliance Factory A Factory B Factory C
Refrigerators 8 10 14
Dishwashers 16 12 10
Stoves 10 18 6

Answer 1

To fulfill the order of 110 refrigerators, 150 dishwashers, and 114 stoves, Factory A should be scheduled for 6 days, Factory B for 6 days, and Factory C for 6 days to ensure timely delivery of all appliances.

Given the production rates per day for each product at each factory:

| Factory | Refrigerators | Dishwashers | Stoves |

| A | 8 | 16 | 10 |

| B | 10 | 12 | 18 |

| C | 14 | 10 | 6 |

To fulfill the order for 110 refrigerators, 150 dishwashers, and 114 stoves

Calculate the number of days needed for each factory:

For Refrigerators:

Factory A:
`\( (110)/(8) = 13.75 \)` (approximately 14 days)

Factory B:
`\( (110)/(10) = 11 \)`days

Factory C:
`\( (110)/(14) = 7.85 \)` (approximately 8 days)

For Dishwashers:

Factory A:
`\( (150)/(16) = 9.375 \)` (approximately 10 days)

Factory B:
`\( (150)/(12) = 12.5 \)`(approximately 13 days)

Factory C:
`\( (150)/(10) = 15 \)` days

For Stoves:

Factory A:
`\( (114)/(10) = 11.4 \)`(approximately 12 days)

Factory B:
`\( (114)/(18) = 6.33 \)`approximately 7 days)

Factory C:
`\( (114)/(6) = 19 \)` days

Determine the maximum number of days needed for each factory among all products:

Factory A: 14 days (refrigerators)

Factory B: 13 days (dishwashers)

Factory C: 19 days (stoves)

Therefore, the maximum number of days required among the factories is 19 days for Factory C (stoves).

However, considering all appliances must be delivered together, the minimum scheduling time across all factories becomes the determining factor. In this case, all three factories should be scheduled for **6 days** to fulfill the entire order, as Factory A, with the longest minimum production time.

Thus, the correct scheduling to fulfill the order is 6 days for Factory A, 6 days for Factory B, and 6 days for Factory C.