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Question $6$

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Question text

Consider the following profit maximization LP problem output from the Excel. Based on the sensitivity information provided below in the solution, select the BEST corresponding answer.

What happens if you acquire $2$ additional kilograms of material?

Max $3$X $+5$Y

s$.$t$.1$ X $+2$ Y $<=10$ labour in hours

$6$ X $+6$ Y $<=36$ material available in kg

$8$ X $+4$ Y $<=40$ storage available in sq m

Solution

Decision Variables

X Y

items Produced $24$

Maximize Total Profit $26$

Constraints Amount Used $($LHS$)$ Amount Available $($RHS$)$

labour in hours $10<=10$

material avail in kg $36<=36$

storage avail in sq m $32<=40$

Sensitivity report

Variable Cells

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$B$$18$ items Produced X $20320\mathrm{.}5$

$C$$18$ items Produced Y $40512$

Constraints

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R$.$H$.$ Side Increase Decrease

$B$$23$ labour in hours Amount Used $($LHS$)1021022$

$B$$24$ material avail in kg Amount Used $($LHS$)360\mathrm{.}16673646$

$B$$25$ storage avail in sq m Amount Used $($LHS$)320401$E$+308$

Question $6$Select one:

a$.$

profits increase by $$1\mathrm{.}00$

b$.$

profits decrease by $$2\mathrm{.}00$

c$.$

profits increase by $$0\mathrm{.}33$

d$.$

profits increase by $$0\mathrm{.}50$

e$.$

profits decrease by $$0\mathrm{.}50$

f$.$

profits decrease by $$1\mathrm{.}50$

g$.$

profits increase by $$8\mathrm{.}00$