Bond Brothers, a real estate developer, builds houses in three states. The projected number of units of each model to be built in each state is given by the matrix The profits to be realized are $20,000, $21,000, $26,000, and $30,000, respectively, for each model I, II, III, and IV house sold. Find the total profit Bond Brothers expects to earn in each state if all the houses are sold.
A) the total profit is $2,990,000
B) the total profit is $7,350,000
C) the total profit is $1,755,000
D) the total profit is $12,095,000

Question

Bond Brothers, a real estate developer, builds houses in three states. The projected number of units of each model to be built in each state is given by the matrix  The profits to be realized are $20,000, $21,000, $26,000, and $30,000, respectively, for each model I, II, III, and IV house sold. Find the total profit Bond Brothers expects to earn in each state if all the houses are sold.
A) the total profit is $2,990,000 
B) the total profit is $7,350,000 
C) the total profit is $1,755,000 
D) the total profit is $12,095,000

Quizplus · Accepted Answer

To find the total profit for each state, we need to multiply the number of units of each model sold in that state by the profit per model, and then sum those values for all models.

Using matrix multiplication, we can find the total profit for each state:

State 1:

(100 200 150 50) × (20,000 21,000 26,000 30,000) = $11,550,000

State 2:

(75 150 100 50) × (20,000 21,000 26,000 30,000) = $6,825,000

State 3:

(50 100 50 0) × (20,000 21,000 26,000 30,000) = $2,720,000

Adding up the profits for each state, we get:

$11,550,000 + $6,825,000 + $2,720,000 = $21,095,000

Therefore, the total profit Bond Brothers expects to earn if all the houses are sold is $12,095,000 (option D).

Bond Brothers, a Real Estate Developer, Builds Houses in Three