The vector gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Use dot products to determine the revenue for these two laptops if the price of each is increased by 7%.

Question

The vector  gives the number of units of two models of laptops produced by a company. The vector  gives the prices (in dollars) of the two models of laptops, respectively. Use dot products to determine the revenue for these two laptops if the price of each is increased by 7%.

Quizplus · Accepted Answer

To calculate the revenue, we need to take the dot product of the two vectors - the number of units produced and the prices of the laptops. Let's call the two vectors A and B, respectively.
A = [11ec1854_fd5f_8db6_acfc_5f5ad8d8a887_TBX8702_11]
B = [11ec1854_fd5f_8db7_acfc_e79d42ca5934_TBX8702_11]

To calculate the dot product, we take the sum of the products of corresponding elements in the two vectors. Mathematically,
A · B = (a1 × b1) + (a2 × b2) + ... + (an × bn)

where a1, a2, ..., an are the elements in vector A, and b1, b2, ..., bn are the elements in vector B.

So, we have,
A · B = (11 × 800) + (6 × 1200) = 9800

This means that the current revenue is $9,800.

To calculate the new revenue after the price increase,
1. We need to calculate the 7% increase in the prices. Let's call the new price vectors B1 and B2, respectively.
B1 = 1.07B = [1.07 × 800, 1.07 × 1200] = [856, 1284]
B2 = 1.07B = [1.07 × 900, 1.07 × 1400] = [963, 1498]

2. We need to take the dot product of A with each of the new price vectors to get the new revenues.
New revenue for laptop model 1 = A · B1 = (11 × 856) + (6 × 1284) = 14070
New revenue for laptop model 2 = A · B2 = (11 × 963) + (6 × 1498) = 16389

Therefore, the new total revenue would be $30,459. The answer closest to this value is C) 11ec1854_fd5f_b4ca_acfc_8d30bcb9a39f_TBX8702_11.

The Vector Gives the Number of Units of Two