Red Brand Canners On Monday, September 13, Mr. Michael Gordon, Vice President of operations, asked the Controller William William Cooper, the Sales Manaer Charles Myers, and !an !a n "#cker the Prod#ction Manaer to meet $ith him to disc#ss the amo#nt of tomato prod#cts to pack that season. "he tomato crop, $hich had been p#rchased at plantin, $as beinnin to arri%e at the cannery, and packin operations $o#ld ha%e to be started by the follo$in Monday. &ed 'rand Canners (&'C) $as a medi#m*si+e company that canned and distrib#ted a %ariety of fr#it and %eetable prod#cts #nder pri%ate brands in the $estern states. Cooper and Myers $ere the first to arri%e in Mr. Gordons office. office. "he prod#ction manaer came in a fe$ min#tes later and apoloi+ed for bein late. -e had to pick #p prod#ce inspections latest latest #ality estimate of the incomin tomatoes. /t $as estimated estimated abo#t 02 of o f the crop $as rade 4 #ality and the remainin portion of the 3 million po#nd crop $as rade '. Gordon asked Myers abo#t the demand for tomato prod#cts for the comin comin year. Myers replied that they co#ld sell all of the $hole canned tomatoes they co#ld prod#ce, b#t he e5pected tho#h a limited demand for tomato 6#ice and tomato paste. -e then passed aro#nd the latest demand forecasts, $hich is sho$n in 75hibit 1. -e reminded the ro#p that the sellin price has been set in liht of the lon*term marketin stratey of the company, and potential sales ha%e been forecasted at these prices. p rices. 'ill Cooper, after lookin at Myers estimates of demand said that it looked like the company 8sho#ld do #ite # ite $ell on the tomato crop this year9. With the ne$ acco#ntin system that had been set #p, he has been able to comp#te the contrib#tion for each prod#ct, and accordin to his analysis the incremental profit on the $hole tomatoes $as reater than for any other tomato prod#cts. /n May, after &'C had sined contracts areein to p#rchase the ro$ers prod#ction at an a%erae deli%ered price of :.1; per po#nd, Cooper had comp#ted the tomato prod#cts contrib#tions contrib#tions (see 75hibit 0). !an "#cker bro#ht to Coopers attention that altho#h there $as ample prod#ction capacity, it $as impossible impossible to prod#ce all $hole $h ole tomatoes beca#se too small portion of the tomato crop $as 4 #ality. &'C #sed a n#merical scalin to record the #ality of both ra$ prod#ce and prepared prod#cts. "his scale ran from to 1, $ith the hiher n#mber representin better #ality. &atin tomatoes accordin to this scale, rade 4 tomatoes a%eraed < points per po#nd and rade ' tomatoes a%eraed = points per po#nd. "#cker noted that the a%erae inp#t #ality for canned $hole tomatoes $as ; points, and for 6#ice > points per po#nd. Paste co#ld be made entirely from rade ' tomatoes. "his meant that $hole tomato prod#ction $as limited to ;, po#nds. Gordon stated that this $as not a real limitation. -e had been recently solicited to p#rchase ;, po#nds of rade 4 tomatoes at :.;= per po#nd and at that time he t#rned do$n the offer. -e felt, ho$e%er, that the tomatoes $ere still a%ailable.
Myers, $ho had been doin some calc#lations, said that altho#h he areed that the company 8sho#ld do #ite $ell this year9 it $o#ld not be by cannin $hole tomatoes. /t seemed to him that the tomato cost sho#ld be allocated based on #antity and #ality, rather than by #antity only as Cooper had done. "herefore, he re*comp#ted the marinal profit on this basis (75hibit 3). ?rom his res#lt, &'C sho#ld #se 0,, po#nds of the rade ' tomatoes for paste, and the remainin @, po#nds of rade ' alon $ith all of the >, po#nds of rade 4 tomatoes for 6#ice.
Assignments Answer the following general questions: 1. Why does "#cker state that the $hole tomato prod#ction is limited to ;, po#ndsA (i.e. $here does the n#mber ;, come fromA) 0. What is $ron $ith Coopers s#estion to #se the entire crop for $hole tomatoesA 3. -o$ does Myers reach the concl#sion that the company sho#ld #se 0,, po#nds of rade ' tomatoes for paste and the rest of the rade ' and rade 49 tomatoes to prod#ce 6#iceA What is $ron $ith Myers reasoninA @. Myers calc#lated the tomato cost for Whole "omato cans to be :@.@B per can (see 75hibit 3). 75plain ho$A "his fi#re is a bit ro#nded (from @.@><). Set up a linear programming model and solve it with Solver. Answer sensitivity analysis questions: =. Witho#t incl#din the possibility of the additional p#rchases s#ested by Gordon, form#late as an P the problem of determinin the optimal cannin policy. Dse the appropriate parameters from one of the e5hibits sho$n belo$. >. 4ns$er the follo$in #estions abo#t the optimal sol#tionE a. -o$ m#ch of each tomato rade $ill be #sed for the prod#ction of each prod#ctA b. -o$ m#ch of each prod#ct is prod#cedA c. What is the act#al a%erae #ality per po#nd of the $hole tomato and the 6#iceA d. What is the net profit obtained after nettin o#t the cost of the cropA B. 4ns$er the follo$in sensiti%ity analysis #estionsE a. /s additional p#rchase of #p to ;, po#nds of rade 4 sho#ld be #ndertaken at a price of :.;=A Can yo# tell e5actly ho$ m#ch sho#ld be p#rchasedA b. S#ppose the Market &esearch !epartment feels that it can increase demand for the 6#ice prod#ct by 0=, cases by startin an ad%ertisin campain. -o$ m#ch sho#ld &'C be $illin to pay for s#ch a campainA c. S#ppose the price of 6#ice increased 3 cents per case. What $ill happen to the optimal sol#tionA d. S#ppose an additional lot of =, po#nds of rade ' tomatoes becomes a%ailable. -o$ m#ch sho#ld &'C be $illin to pay for this lotA Model Modifications:
;.
-o$ sho#ld yo#r model be modified to incl#de the possibility of the additional p#rchases s#ested by GordonA ?ind at $hich cost per po#nd it becomes optimal to p#rchase
additional amo#nt of rade 4 tomatoes. 4ss#me the additional amo#nt a%ailable is ;, po#nd. Sol%e the ne$ Exhibit 1: Demand forecasts and usage model and state the Demand Pound optimal sol#tion. Product Forecast (cases) per case ;. S#ppose #n#sed Whole Tomato 800,000 18 tomatoes co#ld be sold Tomato Juice 50,000 20 at 1; cents per po#nd. Tomato Paste 80,000 25 Chane yo#r form#lation and resol%e.
Exhibit 2: Cooper's product item profitabilit Product Selling price Variable costs: Direct labor Variable OHD Variable Selling Pacaging Tomato Total Variable costs !ontribution "ess #llocated OHD $et Pro%it
Whole Tomatoes
Tomato Juice
Tomato Paste
!12
!1"#50
!11#$0
"#5$ 0#2 1#2 2#1 "#2$ 10#8 1#2 0#8$ 0#"&
"#%& 1#08 2#55 1#%5 "#& 1"#1$ 0#"& 0#&" (0#2
1#&2 0#8 1#1$ 2#"1 $#5 10#"5 1#05 0#&% 0#"&
Exhibit ": )ers' )arginal *nalsis + Cost per pound of '*' tomato in cents - Cost per pound of '.' tomato in cents /1 &00,000+2,$00,000- /",000,000/18cent /2
G
F =
<
=
+ 2#%" cents - 15#52 cents Product Selling Price Variable cost (e&cluding Tomato cost) Tomato cost 'arginal Pro%it
Whole Tomatoes
Tomato Juice
Tomato Paste
!12#00 !#5&
!1"#50 !%#5$
!11#$0 !5#85
$#$$ !$#$ /!0#0"
"#%& !"#2 !0#2$
5#5" !"#%0 !1#&5