Question 1 A

A company manufactures two types of boxes, corrugated and ordinary cartons. The boxes undergo two major processes: cutting and pinning operations. The profits per unit are $6 and $4 respectively.Eachcorrugatedboxrequires2minutesforcuttingandeachcartonrequires3minutes for cutting, whereas each corrugated box requires 2 minutes for pinning and each carton requires 1 minute for pinning. The available cutting time is 120 minutes and total pinning time is 60 minutes. Determine the optimum quantities of the two boxes to maximize theprofits.

1. Formulate a linear programming model that can be used to determine the quantities of the two boxes that should be produced in order to maximize total profit contribution
2. Graph the feasible region.
3. Determine the coordinates of each extreme point.
4. What is the optimal solution.
5. Solve in excel using the template provided.

Question 1 B

Groovy Juice Mixers produces juices, Tropical breeze and Guava Jive. These Juices are both made by blending three ingredients, Grape, guava and Papaya. A certain level of flexibility is permitted in the formulae for these products. The allowable percentages, along with revenue and cost data, are given in the following table. Up to 60 gallons of Grape, 80 gallons of Guava and 60 gallons of papaya could be purchased. Groovy can sell as much of these juices as itproduces.

Juices	Ingredient Grape	Ingredient Guava	Ingredient Papaya	Sales price per Gallon
Tropical Breeze		At most 25% At least 20%	At most25% At least 20%	8
Guava Jive		At most 50% at least 40%	At most 5%	7
Cost per gallon	1.5	2.5	1.5

1. Formulate an LP whose objective is to maximise the net profit from the sale of the juices.

Question 3 A

A private bank has installed an ATM in the city bazaar area. It was found that the time between an arrival and completion of transaction varies from one minute to seven minutes. The arrival and servicedistribution times are givenbelow.

\f