Part I: Linear Programming

Las Cruces Quality Inc. has two grades of inspectors, $1$ and $2,$ who are to be assigned for a

quality control inspection. It is required that at least $1,800$ pieces be inspected per $8-$hour

day. Grade $1$ inspectors can check pieces at the rate of $25$ per hour, with an accuracy of

$98\%.$ Grade $2$ inspectors check at the rate of $15$ pieces per hour, with an accuracy of $95\%.$

The wage rate of a Grade $1$ inspector is $$16\mathrm{.}00$ per hour, while that of a Grade $2$ inspector

is $$12\mathrm{.}00$ per hour. Each time an error is made by an inspector, the cost to the company is

$$8\mathrm{.}00.$ The company has available for the inspection job eight Grade $1$ inspectors, and ten

Grade $2$ inspectors. The company wants to determine the optimal assignment of inspectors,

which will minimize the total cost of the inspection.

a$.$ Formulate a linear programming model to determine the optimal assignment of

inspectors $($Ignore any integer restrictions$).$ Be sure to define decision variables

$(1$ point$).$

b$.$ Use the graphical method to solve this problem $(1$ point$).$

c$.$ Use LINDO$/$LINGO $($or other LP solver$)$ to find the optimal solution and describe it

briefly in "plain English" $(1$ point$).$

d$.$ Add integer restrictions to the formulation in part $($a$),$ and solve using

LINDO$/$LINGO $($or other LP solver$).$ Compare the new optimal solution with the

one in part $($a$).$ What has been changed? $(1$ point$)$