Question

Suppose you plan to go out for a picnic during spring break. You plan to bring sandwiches, fruits, and drinks. But you only have one picnic basket that can only hold a certain capacity. Each of the items has a value and a size, and you cannot hold all your items in the basket. The picnic basket can hold a total size of 17. Given that the size and the value of items are as follows, how many of each item should you bring to maximize the total value?

Size Value
Sandwich 9 6
Fruit 3 4
Drink 4 6
a) List and explain carefully what the decision variables are.
b) Write out the objective function.
c) Write out the constraints.
d) Write the linear program.
e) Solve the Linear Programming problem using excel. Show your results.

Answer 1

e) z (max) = 24

x₁ = x₂ = 0 x₃ = 4

Explanation:

a) The problem requires maximizing the total value from sandwich fruits and drink, therefore the objective function is associated to the sum of the values of each value.

We have three variables xi ( x₁, x₂, x₃ ) the values of sandwich, fruits and drink, and we have to maximize such quantities subject to the constraint of size (the capacity of the basket)

b) z = 6*x₁ + 4*x₂ + 6*x₃ Objective Function

Constraint :

basket capacity 17

9*x₁ + 3*x₂ + 4*x₃ ≤ 17

General constraints:

x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers

e) z (max) = 24

x₁ = x₂ = 0 x₃ = 4

NOTE: Without the information about fractional or decimal feasible solution we decided to use integers solution