The Excel Solver was applied to a product$-$mix problem and the solution as well as the ranging of the solution is presented below. Based on the said information answer the questions listed below.

A B C D E RHS

$013\mathrm{.}7272732089\mathrm{.}6363646\mathrm{.}5454545$

Maximize $24352635294327\mathrm{.}545455$

RM $156574836<=836$

RM $224534450<=450$

RM $343325313\mathrm{.}1818182<=330$

Process $1410170784\mathrm{.}7272727<=1100$

Process $212601381300<=1300$

Process $312424312\mathrm{.}9090909<=400$

Demand A $100000<=53$

Demand B $0100013\mathrm{.}72727273<=62$

Committed vol. $$ C $0010020>=20$

Demand D $0001089\mathrm{.}63636364<=90$

Demand E $000016\mathrm{.}545454545<=50$

Storage $141075915\mathrm{.}0909091<=1242$

Variable Cells

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$C$$6$ A $0-0\mathrm{.}75240\mathrm{.}751$E$+30$

$D$$6$ B $13\mathrm{.}727272730350\mathrm{.}6255\mathrm{.}0125$

$E$$6$ C $200269\mathrm{.}1136363641$E$+30$

$F$$6$ D $89\mathrm{.}6363636403510\mathrm{.}0250\mathrm{.}75$

$G$$6$ E $6\mathrm{.}5454545450298\mathrm{.}0588235291$

Constraints

Final Shadow Constraint Allowable Allowable

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

$H$$16$ Committed vol. $$ C $20-9\mathrm{.}113636364200\mathrm{.}413\mathrm{.}96226415$

$H$$17$ Demand D $89\mathrm{.}636363640901$E$+300\mathrm{.}363636364$

$H$$18$ Demand E $6\mathrm{.}5454545450501$E$+3043\mathrm{.}45454545$

$H$$19$ Storage $915\mathrm{.}0909091012421$E$+30326\mathrm{.}9090909$

$H$$8$ RM $18363\mathrm{.}113636364836421\mathrm{.}14285714$

$H$$9$ RM $24503\mathrm{.}90909090945010\mathrm{.}277777781\mathrm{.}333333333$

$H$$10$ RM $3313\mathrm{.}181818203301$E$+3016\mathrm{.}81818182$

$H$$11$ Process $1784\mathrm{.}7272727011001$E$+30315\mathrm{.}2727273$

$H$$12$ Process $213000\mathrm{.}1136363641300457\mathrm{.}6$

$H$$13$ Process $3312\mathrm{.}909090904001$E$+3087\mathrm{.}09090909$

$H$$14$ Demand A $00531$E$+3053$

$H$$15$ Demand B $13\mathrm{.}727272730621$E$+3048\mathrm{.}27272727$

A subcontractor is willing to produce $12$ units of Product C for us but charges us a unit cost that is about P$8\mathrm{.}00$ higher than our current cost to produce Product C$.$ Should we take the offer? $["$Yes$.$ Product C has no reduced cost.", $"$No$.$ The extra cost of P$8\mathrm{.}00$ is lesser than the negative dual value of $-$P$9\mathrm{.}11.","$No$.$ It is more expensive to subcontract by P$8\mathrm{.}00.",$ "Yes. The extra cost of P$8\mathrm{.}00$ is lesser than the negative dual value of $-$P$9\mathrm{.}11."]$

A buyer wants us to produce Product A and is willing to give us a premium of P$1\mathrm{.}00$ per unit. Should we consider the offer? Explain. $["$Yes as any premium will increase profit.", $"$No as the premium of P $1\mathrm{.}00$ is greater than the reduced cost of P $0\mathrm{.}75.","$No as Product A is nonbasic variable.", "Yes as the premium of P $1\mathrm{.}00$ is greater than the reduced cost of P $0\mathrm{.}75."]$

If you had minimal funds for the business, where will you spend majority of it on$?$ The purchasing department, the marketing department, the operations department? Show basis for decision. $["$Majority of it will be invested in the marketing department considering that demand for products have the higher slacks.", "Majority of it will be invested in processes to improve efficiency.", "Majority of it will be invested in the purchasing department considering that raw materials have the higher dual values.", "Majority of it will be invested in the storage considering that the has the highest slack."$]$

Competition may force you to reduce the price of Product B by P$5\mathrm{.}00.$ Will this affect our optimal product mix? Why or why not? What about our objective function value? $[$ Select $]["$Optimal mix and profit will change with the change in the contribution margin of Product B considering it is a basic variable.", "Optimal mix and profit will remain the same as the margin of $30$ is still within the allowable range.", "Optimal mix will remain the same as the margin of $30$ is still within the allowable range. We are not certain if profit will be reduced.", "Optimal mix will remain the same as the margin of $30$ is still within the allowable range. Profit, however, will be reduced."$]$

If you have to choose, which of these two scenarios would you prefer: $($a$)$ Reduction of the committed volume for Product C from $20$ units to $15$ units or $($b$)$ increase of available Raw Materials $1$ by $4$ units and Raw Materials $2$ by $10$ units? Provide computations to support choice. $[$ Select $]["$Both options are equally attractive.", "Second option as total benefits from second option are higher by about $5\mathrm{.}98.",$ "First option as total benefits from first option are higher by about $5\mathrm{.}98.","$We have insufficient information to compare two options."$]$