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 $$2400,$ and the cost required to set up the production line for the $6-$cylinder connecting rods is $$3000.$ Manufacturing costs are $$15$ for each $4-$cylinder connecting rod and $$20$ 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 $58006-$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

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.

fill in the blank $1$

$0$

x$4$

$<=$

fill in the blank $3$

$8000$

s$4$

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 $5800$ units.

fill in the blank $4$

$1$

x$6$

$<=$

fill in the blank $6$

$5800$

s$6$

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

fill in the blank $7$

$0$

x$4$

$<=$

fill in the blank $9$

s$4$

fill in the blank $10$

$1$

x$6$

$<=$

fill in the blank $12$

s$6$

fill in the blank $13$

s$4+$ fill in the blank $14$

s$6$

$<=$

fill in the blank $16$

$1$

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

Min fill in the blank $17$

x$4+$ fill in the blank $18$

x$6+$ fill in the blank $19$

s$4+$ fill in the blank $20$

s$6$