Ho many of each product can be carried?

Question

The Collin Freight Company has an order for three products to be delivered to a destination. Product 1 requires 10 cubic feet, weighs 10 pounds, and has a value of $100. Product 2 requires 8 cubic feet, weighs 20 pounds, and has a value of $20. Product 3 requires 20 Cubic feet, weighs 40 pounds, and has a value of $200. if the carrier can carry 6000 cubic feet, 11000 pounds, and is insured for $36900, how many of each product can be carried?

Answer 1

A , B, C are the amounts of each product

 

 10A + 8B + 20C = 6000 <--- volume constraints

 

 10A + 20B + 40C = 11000  <---- weight constraints

 

100A + 20B + 200C = 36900  <---- $$$$

 

 

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pairs the first two equations:

 

10A + 8B + 20C = 6000

10A + 20B + 40C = 11000

 

Subtracts first from the second:  12B + 20C = 5000

                                                 3B  + 5C = 1250<--- labels this equation ALPHA

 

 

Pairs the 2nd and 3rd equations:

 

10A + 20B + 40C = 11000 

100A + 20B + 200C = 36900

 

 

Multiplies the top equation by 10:

100A + 200B + 400C = 110000 <---- weight constraints

100A + 20B + 200C = 36900 <---- $$$$

 

Subtracts them:

  180B + 200C = 73100

   18B + 20C = 7310

   9B + 10C = 3655 <--- labels this equation BETA

 

 

ALPHA:   3B + 5C = 1250

BETA:    9B + 10C = 3655

 

Multiplies ALPHA by 3:

 

  9B + 15C = 3750

  9B + 10C = 3655

 

  Subtracts them:

          5C = 95

           C = 95/5 = 19

 

Plugging into BETA:   9B + 10(19) = 3655

                                9B = 3655 - 190

                               B = 385

 

Plugs into original first equation:

 10 A + 8(385) + 20(19) = 6000 

A=254

 

A=254

B=385

C=19