Problems

$in$ cheaper automobiles. For the next week, the company has orders for $100$ units $of$

model A and $150$ units $of$ model $B.$ Both model A and model $B$ parts are manufac$-$

tured $at$ a DCI plant $in$ Newark, New Jersey. Each model A part requires $4$ minutes $of$

injection$-$molding time and $6$ minutes $of$ assembly time. Each model $B$ part requires

$3$ minutes $of$ injection$-$molding time and $8$ minutes $of$ assembly time. For next week,

the Newark plant has $600$ minutes $of$ injection$-$molding time available and $1080$ minutes

$of$ assembly time available. The manufacturing cost $is$ $$10$ per unit for model A and

$$6$ per unit for model $B.$ Depending $on$ demand and the time available $at$ the Newark

plant, DCI occasionally purchases units $of$ one $or$ both models from $an$ outside sup$-$

plier $in$ order $to$ fill customer orders that could not $be$ filled otherwise. The purchase

$costis$ $$14$ for each model A part and $$9$ for each model $B$ part. Management wants

$to$ develop a minimum cost plan that will determine how many cases $of$ each model

should $be$ produced $at$ the Newark plant and how many cases $of$ each model should

$be$ purchased. The following decision variables were used $to$ formulate a linear

programming model for this problem:

$AM=$ number $of$ model A parts manufactured

$BM=$ number $of$ model $B$ parts manufactured

$AP=$ number $of$ model A parts purchased

$BP=$ number $of$ model $B$ parts purchased

Chapter $3$ Linear Programming: Sensitivity Analysis and Interpretation $of$ Solution

The linear programming model that can $be$ used $to$ solve this problem $isas$ follows:

Min $10AM+6BM+14AP+9BP$

$s.t.$

$1AM+,+1AP+=100$ Demand for model $A$

$1BM+,1BP=150$ Demand for model $B$

$4AM+3BM,600$ Injection molding time

$6AM+8BM,1080$ Assembly time

$AM,BM,AP,BP0$

The computer solution $is$ shown $in$ Figure $3\mathrm{.}18.LO2,3,5$

$a.$ What $is$ the optimal solution and what $is$ the optimal value $of$ the objective function?

$b.$ Which constraints are binding?

$c.$ What are the dual values? Interpret each.

$d.If$ you could change the right$-$hand side $of$ one constraint $by$ one unit, which one

would you choose? Why?