Recall the Tom's, Inc, problem $($Chapter $2,$ Problem $28).$ Letting

$W=$ jars $of$ Western Foods Salsa

$M=$ jars $of$ Mexico City Salsa

leads to the formulation:

Max $14+1\mathrm{.}25M$

$s.t.$

$5W+7M4480$ Whole tomatoes

$3W+1M2080$ Tomato sauce

$2W+2M1600$ Tonato paste

$W,M0$

The computer solution is shown in Figure $3\mathrm{.}15.$

a$.$ What is the optimal solution, and what are the optimal production quantities?

b$.$ Specify the ebjective function ranges.

FIGURE $3\mathrm{.}15$ THE SOLLUTION FOR THE TOM'S, INC, PROBLEM

Yarlable

Value

$560\mathrm{.}00000$

$240,00000$

Slack$/$Surplus

$0\mathrm{.}00000$

$160\mathrm{.}00000$

$0\mathrm{.}00000$

Objective

Variable

$q,$

$q,$

$q,$

$\backslash$table$[[1,4480\mathrm{.}00000],[2,2080\mathrm{.}00000],[3,1600\mathrm{.}00000]]$

Reduced Cost

$0\mathrm{.}00000$

$0\mathrm{.}00000$

Dual value

$0\mathrm{.}12500$

$0\mathrm{.}00000$

$0\mathrm{.}28750$

Al$1$owable

Increase

$q,$

$0\mathrm{.}25000$

D$.15000$

Aliconable

Decrease

$0\mathrm{.}10714$

$0\mathrm{.}25000$

Allowable

Allowable

Increase

Decrease

$1120,00000$ Infinite $40\mathrm{.}00000q,$

$160\mathrm{.}00000$

$160\mathrm{.}00000$

$320\mathrm{.}00000$