Linear program

Question

Question 1

Giapetto’s Woodcarving, Inc. manufactures two types of toys: soldiers and trains. Each soldier sold generate $4.00 in profit while each train generates $2.50 in profit. The manufacture of wooden soldiers and trains requires two types of skilled labor: carpentry and finishing. A soldier requires 3 hours of finishing labor and 2 hour of carpentry labor. A train requires 2 hour of finishing labor and 2 hour of carpentry. Each week, Giapetto can obtain all the needed raw materials but only 120 finishing hours and 80 carpentry hours. Demand for trains is unlimited, but at most 25 soldiers are bought each week. Help Giapetto to maximize his profit.

a) Formulate the linear programming model for the problem.
b) Use the Graphical method to find the optimal solution. Show all steps.
c) Use Excel Solver or Lindo to solve the model you formulated. Copy and paste your spreadsheet and the Answer report in its entirety from Excel OR your Lindo input and output.

Answer 1

Let s = the number of soldiers produced each week and t = the number of trains,  The Profit equation is:

 

P = $4s + $2.5t

 

The constraints are:

 

3s + 2t ≤ 120  (No more than 120 hours of finishing labor available per week)

2s + 2t ≤ 80    (No more than 80 hours of carpentry labor available per week)

0 ≤ s ≤ 25       (No more than 25 soldiers will be bought)

t ≥ 0              (Number of trains produced is greater than or equal to 0)

 

Plot these inequalities on a graph.  Your feasible region will have 4 vertices.  Read the coordinates of each vertex and plug the values into the Profit equation to find the combination of soldiers and trains that maximizes profit.