A granite installation company schedules its services based on the installation space. It schedules 3 hours for a standard kitchen installation and 1 hour for a standard bathroom installation. The company schedules a maximum of 12 hours of installation time per day, and performs no more than 3 bathroom installations per day. The average profit for a bathroom installation is $1200, and the average profit for a kitchen installation is $3300.

Part A: How many kitchen and bathroom installations should the company schedule per day in order to maximize profit?

Part B: How much money does the company earn per day if it maximizes profit?

Part A

3 Bathroom and 3 Kitchen

Part B.

$13,500

Step-by-step explanation:

Bathroom per day = 3

Average profit of Bathroom = $1,200 per hour

Kitchen per day = (12 hours - 3 hours) / 3 = 3 kitchen

Average Profit from Kitchen = $3,300 / 3 = $11,00 per hour

As the company cannot do more than 3 bathrooms which has higher per hour average profit, the remaining 9 hours will be utilized for Kitchen Installation.

Part A.

Company will do 3 Bathrooms and 3 Kitchens in order to maximize the profit under given condition.

Part B.

Total Earning = ($1,200 x 3) + ($1,100 x 9) = $3,600 + $9,900 = $13,500

The company will earn Average profit of $13,500.

Answer: Part A; The company should schedule 3 Kitchen installations and 3 Bathroom installations

Part B; The company would earn $13500 per day if it maximizes profit.

Step-by-step explanation: The first thing to note is that the company has a schedule of 12 hours of installation per day at the maximum. Also they cannot carry out more than 3 bathroom installations per day and they have scheduled each bathroom installation to take one hour. This means they have nine hours left for Kitchen installations. Each kitchen installation takes three hours, and that means they cannot exceed three kitchen installations. So for the twelve hours maximum which they have scheduled, it would be best if they apportioned it's as follows;

Kitchen Installations: 3 (x 3hrs) = 9hrs

Bathroom Installation: 3 (x 1hr) = 3hrs

If the profit per kitchen installation is given as $3300, and that of bathroom installation is given as $1200, then the maximum profit they should be realizing daily is given as,

Profit = 3 x (3300) + 3 x (1200)

Profit = 9900 + 3600

Profit = 13500

Their maximum profit would be $13,500