Assignments Answer the following general questions: 1. Why does Tucker Tucker state state that the the whole tomato tomato producti production on is limited limited to 800,000 800,000 pounds? (i.e. where does the number 800,000 come from?) . What is wron! wron! with with "ooper#s "ooper#s su!!est su!!estion ion to use the the entire entire crop for whole whole tomatoes tomatoes?? $. %ow does &yers &yers reach the the conclusion conclusion that that the company company should should use use ,000,000 ,000,000 pounds pounds of !rade '# tomatoes for paste and the rest of the !rade '# and !rade '* tomatoes to produce +uice? What is wron! with &yers reasonin!? . &yers calcul calculated ated the tomato tomato cost cost for Whole Whole Tom Tomato ato cans to to be -. per can can (see /hibit $). /plain how? This fi!ure is a bit rounded (from .2). Set up a linear programming model and solve it with Solver. Answer sensitivity analysis questions: 3. Without Without includin! the possibility of the additional purchases p urchases su!!ested by 4ordon, formulate as an 56 the problem of determinin! the optimal cannin! policy. 7se the appropriate parameters from one of the ehibits shown below. . nswer the followin! uestions about the optimal solution9 a. %ow mu much of each tomato ato !r !rade ade wi will be be us used fo for the the produ oduction of of ea each product? b. %ow much of each product is produced? c. What hat is is th the ac actual a: a:era!e u uality per per pound of th the wh whole tom tomat ato o an and th the +uice? d. What hat is is th the ne net pr profi ofit ob obtained af after ne nettin! out th the co cost of of th the cr crop? . nswer the followin! sensiti:ity analysis uestions9 a. ;s ad addit ditional pu purchase of of up up to to 80 80,000 pound unds of of !r !rade ade ' '# shou hould be be undertaken at a price of -0.083? "an you tell eactly how much should be purchased? b.
epartment feels that it can increase demand for the +uice product by 3,000 cases by startin! an ad:ertisin! campai!n. %ow much should =" be willin! to pay for such a campai!n? c.
8.
%ow %ow shou should ld your your mode modell be be modi modifie fied d to to incl include ude the the poss possibi ibilit lity y of of the the additi additiona onall purc purchas hases es su!!ested by 4ordon? ind at which cost per pound it becomes optimal to purchase additional amount of !rade '# tomatoes. ssume the additional amount a:ailable is 80,000 pound.
Exhibit 1: Demand forecasts and usage Product Whole Tomato Tomato Juice Tomato Paste
Demand Forecast (cases)
Pound per case
800,000 50,000 80,000
18 20 25
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,$00,000- /",000,000/18cent /2
A
@ =
2
3
+ 2#%" cents - 15#52 cents Product Selling Price Variable cost (e&cluding Tomato cost) Tomato cost 'arginal Pro%it
Whole Tomatoes
Tomato Juice
Tomato Paste
!12#00 !#5&
!1"#50 !%#5$
!11#$0 !5#85
$#$$ !$#$ /!0#0"
"#%& !"#2 !0#2$
5#5" !"#%0 !1#&5
