Question

A freight company has shipping orders for two products. The first product has a unit volume of 10 cu ft and weighs 50 lb. The second product's unit volume is 3 cu ft, and it weighs 40 lb. If the company's trucks have 2,320 cu ft of space and can carry 21,600 lb, how many units of each product can be transported in a single shipment with one truck using the entire volume and weight capacity?

Answer 1

Answer:

Number of units of first product = 112

Number of units of second product = 400

Step-by-step explanation:

Given that there are two products which are to be shipped.

First product details:

Unit volume = 10 cu ft

Weight of one unit = 50 lb

Second product details:

Unit volume = 3 cu ft

Weight of one unit = 40 lb

Total volume that can be carried by a truck = 2320 cu ft

Total weight that can be carried by a truck = 21600 cu ft

To find:

The number of units of each product that can be transported in one shipment in the truck?

Solution:

Let number of units of first product = $x$

Let number of units of second product = $y$

We can write down two linear equations in two variables here and solving them will give us the answer we are required to find.

As per question statement, the equations can be written as:

$10x+3y = 2320 ...... (1)\\50x+40y = 21600\\\Rightarrow 5x+4y = 2160...... (2)$

Multiplying equation (2) with 2 and subtracting equation (1) from it:

$8y - 3y = 4320-2320\\\Rightarrow 5y = 2000\\\Rightarrow \bold{ y = 400}$

By equation (1):

$10x+1200 = 2320\\\Rightarrow 10x = 1120\\\Rightarrow \bold{x = 112}$

Answer is:

Number of units of first product = 112

Number of units of second product = 400