The Sunshine Food Processing Company produces three commercial grade canned fruit products - mixed fruit, fruit cocktail, and fruit delight. The main ingredients in each of the three products are pears and peaches. Each product is produced in lots and must go through three processes - mixing, canning, and packaging. The company can easily sell all that it can make. The company uses linear programming to plan its quarterly production. The company has a contract with Lightshine Company to supply at least 15,000 cans of fruit delight. The resource requirements and profit margin for all three products are shown below. Any cost not listed or mentioned in the problem can be considered sunk.

Product	Pears(lbs)	Peaches(lbs)	Mixing(hrs)	Canning(hrs)	Packaging(hrs)	Profit ($/can)
Mixed fruits	20	10	1	1	2	10
Fruit cocktail	10	20	2	1	1	6
Fruit delight	16	16	2	1	1	8
Availability	320,000	400,000	43,000	60,000	40,000

Let X1, X2, X3 be the number of cans (in 1000s) of the three products to be produced during the next quarter.

Max 10 X1 + 6 X2 + 8 X3 (profit in 1000s of $)

st 20 X1 + 10 X2 + 16 X3

10 X1 + 20 X2 + 16 X3

X1 + 2 X2 + 2 X3

X1 + X2 + X3

2 X1 + X2 + X3

X3 > 15 (Lightshine demand in 1000s of cans)

X1, X2, X3 > 0 (Nonnegativity)

Using the attached Excel output to answer the following questions. No need to run the Solver.

a) What are the units of shadow prices of the pears and packaging constraint?

b) Which of the resources constrains the total contribution margin?

c) What is the maximum price the company would be willing to pay for additional lbs of peaches? How much should be purchased? Justify

d) A fruit grower is offering to sell pears at $0.467/lb. Will you buy additional quantities? If so, how much? Justify your decision.

e) The company can purchase a new mixing machine that would increase the available mixing time from 43,000 to 45,000 hours. How much is this additional capacity worth?

f) The company can also purchase a new packaging machine that would increase the available packaging time from 40,000 to 50,000 hours. Would this impact the optimal solution?

g) Due to a problem with the fruit supplier, only 320,000 pounds of peaches will be available. Will this impact the optimal product mix? h) If the manager were to attempt to secure additional units of only one of the resources, what should it be? Justify.

i) If the company revised the selling price of fruit cocktail so that the profit margin increased from $6 to $10, would the optimal solution change?

j) There is an opportunity to renegotiate the contract of fruit delight with Lightshine Company. What is your recommendation?

Sunshine Food Company DECISION VARIABLES Product Production Qty (1000s of can Mixed Fruit Fruit Cocktail Fruit Delight 1.00 6.00 15.00 OBJECTIVE COEFFICIENT Unit Profit Margin 01 Total Prof (1000s of $) 166 10 B a 10 1 2 Usage 16.00 16.00 2.00 1.00 1.00 1.00 LHS RHS 320.00 320 370.00 $ 400 43.00 43 22.00 60 23.00 40 15.00 15 1 0 Original Value Final Value 166 CONSTRANTS Resource Pears (1000s olib Peaches (1001s of Ibis 10 Mixing (1000s of hours) Canning (100s of hour 1 Packaging Mots of hours 2 Lightshine Demand (1000s of cans Microsoft Excel 18. Anwer Report Objective Cel Mas) Neme SESS Unit Psal. Marin 15. Total Pradt 9000) Variable Cells Nene Sess Production y 11000 of cons. Med Fruk 135 Production Cy11000s of cons TO SDS Production day 11000s of cons. For Corros Call Name BE11 PLH SES 12 Peaches (000site LHS SES13 Micing (1000s of hours) Les SES14 Canning 1000s of hours) Les SES 15 Packaging 1000 LHS SES 16 Lshtatine Derrand 1000s of LHS Original Value 0.00 0.00 Final Value 1 Corin 8.00 Core 160 L Microsoft Excel 15.0 Sensitivity Report Variable Calls Slack 30 Call Value Formula Status 329.00 $E$1110111 30.00 SE 512=5G512 Med Binding 43.00 SE 51313 Binding 22.00 SE 1514 Binding 23.00 SE 515-5G515 Not Binding 15.00 SES16-=$G$16 binding Cell Name $895 Production Qty (1000s of cars) Mixed Fruit $C$5 Production Qty (1000s of cans) Fruit Cocktail $0$5 Production Qty 1000s of cansFruit Delight Final Value 1 6 15 Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 10 2 2 0 14 0 8 08 1E +30 36 000 Constraints Cell Name SE511 Pears (1000s of los) LHS $E$12 Peaches (1000s of its) LHS SES13 Maing (1000s of hours) LHS SE$14 Canning (1000s of hours, LHS SE515 Packaging (1000s of hours) LHS SE516 Lightshine Demand (1000s of cana) LHS Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 320 0466676867 320 170 15 370 0 400 1E +30 43 0.667 43 9 22 0 1E430 39 23 0 40 1E+30 17 15 -0.8 15 25 7.5 Sunshine Food Company DECISION VARIABLES Product Production Qty (1000s of can Mixed Fruit Fruit Cocktail Fruit Delight 1.00 6.00 15.00 OBJECTIVE COEFFICIENT Unit Profit Margin 01 Total Prof (1000s of $) 166 10 B a 10 1 2 Usage 16.00 16.00 2.00 1.00 1.00 1.00 LHS RHS 320.00 320 370.00 $ 400 43.00 43 22.00 60 23.00 40 15.00 15 1 0 Original Value Final Value 166 CONSTRANTS Resource Pears (1000s olib Peaches (1001s of Ibis 10 Mixing (1000s of hours) Canning (100s of hour 1 Packaging Mots of hours 2 Lightshine Demand (1000s of cans Microsoft Excel 18. Anwer Report Objective Cel Mas) Neme SESS Unit Psal. Marin 15. Total Pradt 9000) Variable Cells Nene Sess Production y 11000 of cons. Med Fruk 135 Production Cy11000s of cons TO SDS Production day 11000s of cons. For Corros Call Name BE11 PLH SES 12 Peaches (000site LHS SES13 Micing (1000s of hours) Les SES14 Canning 1000s of hours) Les SES 15 Packaging 1000 LHS SES 16 Lshtatine Derrand 1000s of LHS Original Value 0.00 0.00 Final Value 1 Corin 8.00 Core 160 L Microsoft Excel 15.0 Sensitivity Report Variable Calls Slack 30 Call Value Formula Status 329.00 $E$1110111 30.00 SE 512=5G512 Med Binding 43.00 SE 51313 Binding 22.00 SE 1514 Binding 23.00 SE 515-5G515 Not Binding 15.00 SES16-=$G$16 binding Cell Name $895 Production Qty (1000s of cars) Mixed Fruit $C$5 Production Qty (1000s of cans) Fruit Cocktail $0$5 Production Qty 1000s of cansFruit Delight Final Value 1 6 15 Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 10 2 2 0 14 0 8 08 1E +30 36 000 Constraints Cell Name SE511 Pears (1000s of los) LHS $E$12 Peaches (1000s of its) LHS SES13 Maing (1000s of hours) LHS SE$14 Canning (1000s of hours, LHS SE515 Packaging (1000s of hours) LHS SE516 Lightshine Demand (1000s of cana) LHS Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 320 0466676867 320 170 15 370 0 400 1E +30 43 0.667 43 9 22 0 1E430 39 23 0 40 1E+30 17 15 -0.8 15 25 7.5