# Part 2: A toy manufacturer makes three models of a toy robot. The first model requires 10 minutes ea

Part 2:

A toy manufacturer makes three models of a toy robot. The first model requires 10 minutes each for fabrication and packaging and 2 pounds of plastic, the second model requires 12 minutes for fabrication and packaging and 3 pounds of plastic, and the third model requires 15 minutes for fabrication and packaging and 4 pounds of plastic. There are 8 hours of fabrication and packaging time available and 150 pounds of plastic available for the next production cycle. The unit profits are \$4 for each Model 1, \$7 for each Model 2 and \$10 for each Model 3. A minimum of 10 units of Model 2 must be made to fill a previous order.

The problem has been formulated below.

Let       X1 = the number of units of Model 1 to be produced

X2 = the number of units of Model 2 to be produced

X3 = the number of units of Model 3 to be produced

Maximize Z = 4X1 + 7X2 + 10X3

Subject to         10X1 + 12X2 + 15X3 ≤ 480        (fabrication and packaging time, minutes)

2X1 +   3X2 +   4X3 ≤ 150        (pounds of plastic)

X2 ≥ 10        (minimum of X2)

X1, X2, X3 ≥ 0

The problem has been solved using Excel Solver and the output is attached. Answer the questions below.

Questions:

1.         Clearly state the optimal solution to the problem in context.

2.         Which resources are used up and which are not? For those not used up, state the amount left over.

3.         What is the range of optimality for the profit of Model 2? What does it mean?

4.         The profit of Model 3 has fallen to \$8. Do we have to solve the problem again? Why?

5.         If any of the decision variables is not being produced, what has to be done to make it       profitable for production?

6.         What is the range of feasibility for pounds of plastic? What does it mean?

7.         The manufacturer can get additional minutes for fabrication and packaging at a cost of \$0.25 per minute. (a) Should the company get additional minutes for its fabrication and packaging unit?

Give reasons. (b) If the company decides to get more minutes, how many can they get and what will be the additional contribution to profit?

Model1 Model2 Model3 Unit profit 4 7 10 Constraints RHS LHS Fab & pack 480 10 480 12 15 150 Plastic 126 2 3 10 Model2 min 10 1 310 Max Profit Needed 10 Variable Cells Reduced Objective Allowable Allowable Coefficient Increase Decrease 1E+30 Final Value Cost Cell Name 2.666667 0 -2.66667 Units requir Units requir \$B\$9 \$C\$9 \$D\$9 1E+30 1 7 0 10 1.25 1E+30 10 0 24 Units requir Constraints Shadow Constraint Allowable Allowable Increase Decrease Final R.H. Side Price Value Cell Name 480 360 90 480 0.666667 \$E\$5 \$E\$6 \$E\$7 Fab & pack 24 1E+30 150 126 Plastic LHS 10 30 10 1 10 Model2 min YAA 4 24