ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 1) Two kinds of crated cargo, A and B, are to be shipped by truck. Each crate of cargo A is 50 cubic feet in volume and weighs 200 pounds, whereas each crate of cargo B is 10 cubic feet volume and weighs 360 pounds. The shipping company charges $75 per crate for cargo A and $100 per crate for cargo B. The

To complete the problem statement it is needed:

1.- the volume and weight capacity of the truck, because these will become the constraints.

2.- In order to formulate the objective function we need to have an expression like this:

" How many of each type of crated cargo should the company shipped to maximize profit".

Solution:

z(max)  =  175  $

x  =  1

y  =  1

Assuming  a weight constraint   700 pounds  and

volume constraint  150 ft³ we can formulate an integer linear programming problem ( I don´t know if with that constraints such formulation will be feasible, but that is another thing)

Step-by-step explanation:

crated cargo A   (x)          volume  50 ft³   weigh   200 pounds

crated cargo B   (y)          volume  10 ft³     weigh   360 pounds

Constraints:  Volume     150 ft³

50*x  +  10*y  ≤ 150

Weight contraint:  700 pounds

200*x   +  360*y  ≤ 700

general constraints

x ≥ 0    y ≥ 0  both integers

Final formulation:

Objective function:

z  =  75*x  +  100*y   to maximize

Subject to:

50*x  +  10*y  ≤ 150  

200*x   +  360*y  ≤ 700

x ≥ 0  y  ≥ 0  integers

After 4 iterations with the on-line solver the solution

z(max)  =  175  $

x  =  1

y  =  1