Problem $11-9($Algorithmic$)$ Problem $11-9($Algorithmic$)$

Hawkins Manufacturing Company produces connecting rods for $4-$ and $6-$cylinder automobile engines

using the same production line. The cost required to set up the production line to produce the $4-$

cylinder connecting rods is $$2300,$ and the cost required to set up the production line for the $6-$

cylinder connecting rods is $$3800.$ Manufacturing costs are $$13$ for each $4-$cylinder connecting rod

and $$18$ for each $6-$cylinder connecting rod. Hawkins makes a decision at the end of each week as to

which product will be manufactured the following week. If there is a production changeover from one

week to the next, the weekend is used to reconfigure the production line. Once the line has been set

up$,$ the weekly production capacities are $59006-$cylinder connecting rods and $80004-$cylinder

connecting rods.

Let

$x_4=$ the number of $4-$cylinder connecting rods produced next week

$x_6=$ the number of $6-$cylinder connecting rods produced next week

$s_4=1$ if the production line is set up to produce the $4-$ cylinder connecting rods; $0$ if otherwise

$s_6=1$ if the production line is set up to produce the $6-$cylinder connecting rods; $0$ if otherwise

a$.$ Using the decision variables $x_4$ and $s_4,$ write a constraint that limits next week's production of the

$4-$cylinder connecting rods to either $0$ or $8000$ units.

$x_4.$

b$.$ Using the decision variables $x_6$ and $s_6,$ write a constraint that limits next week's production of the

$6-$cylinder connecting rods to either $0$ or $5900$ units. a$.$ Using the decision variables $x_4$ and $s_4,$ write a constraint that limits next week's production of the

$4-$cylinder connecting rods to either $0$ or $8000$ units.

$x_4$

$54$

b$.$ Using the decision variables $x_6$ and $s_6,$ write a constraint that limits next week's production of the

$6-$cylinder connecting rods to either $0$ or $5900$ units.

$x_6$

$56$

c$.$ Write three constraints that, taken together, limit the production of connecting rods for next week.

$x_4$

S$4$

$x_6$

S$6$

$S_4+S_6$

d$.$ Write an objective function for minimizing the cost of production for next week.

Min

$x_4+$

$x_6+$

$s_4+$ s$6$