Operations Research Answers

There are 200 shirts and 100 pairs of trousers from last season that a retailer wants to get rid of. They've come up with two options, A and B, and are putting them together. Offer A is a $30 set that includes a shirt and a pair of trousers. Offer B is a $50 set that includes three shirts and two pairs of trousers. A total of 20 of Offer A and 10 of Offer B packages must be sold in order for the business to make a profit. Is there a maximum number of packets they need to sell in order to maximize profit?

There are two truck kinds available to a transportation company: Type A and Type B. When comparing Type A with Type B, Type A has an overall volume of 20 m3 with equal portions for refrigerated and non-refrigerated stock, while Type B has an overall volume of 40 m3 with equal sections for both types of stock. 3,000 m3 of refrigerated stock and 4 000 m3 of nonrefrigerated goods must be transported by truck. Type A cars cost P30 per kilometer, whereas Type B cars cost P40 per kilometer. In order to keep rental costs to a low, how many of each kind of truck should the grocer rent?

There are 200 shirts and 100 pairs of trousers from last season that a retailer wants to get rid of. They've come up with two options, A and B, and are putting them together. Offer A is a $30 set that includes a shirt and a pair of trousers. Offer B is a $50 set that includes three shirts and two pairs of trousers. A total of 20 of Offer A and 10 of Offer B packages must be sold in order for the business to make a profit. Is there a maximum number of packets they need to sell in order to maximize profit?

Maximise 1170x1 + 1110x2

Subject to: 9x1 + 5x2 ≥ 500

7x1 + 9x2 ≥ 300

5x1 + 3x2 ≤ 1500

7x1 + 9x2 ≤ 1900

2x1 + 4x2 ≤ 1000

x1, x2 ≥ 0

-Find graphically the feasible region and the optimal solution.

suppose tasty treat wants to introduce two new items in its menu: milkshake and smoothie. The cost to make a single serving of milkshake and smoothie is $60 and $50 respectively. They wants to minimize their cost. Everyday, at least 25 watts of electricity should be used in the kitchen. To make one serving of milkshake and smoothie, 1 watt and 2 watts of electricity is required, respectively. 3 minutes and 2 minutes are required each day to produce a serving of the items using at least 48 minutes by the workers.

Solve the following LP problem by graphical method: Maximise Z = 300X1 + 700X2

Subject to the constraints: X1 + 4X2 ≤ 20 2X1 + X2 ≤ 30 X1 + X2 ≤ 8 And X1, X2 ≥ 0

A firm manufactures two products; the net profit on product 1 is Birr 3 per unit and Birr 5

per unit on product 2. The manufacturing process is such that each product has to be

processed in two departments D1 and D2. Each unit of product1 requires processing for 1

minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes

at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200

minutes at D2. How much of product 1 and 2 should be produced every day so that total

profit is maximum. (solve with graphical method

A large group of students took a test in physics and have a mean of 70 and a standard deviation of 10.If we approximate the distribution of these grades by a normal distribution, what percentage of the students

a) scored higher than 80?

b) should pass the test(grades>=60)?

c) should fail the test(grades<60)?

Maximise 1170x1 + 1110x2

Subject to: 9x1 + 5x2 ≥ 500

7x1 + 9x2 ≥ 300

5x1 + 3x2 ≤ 1500

7x1 + 9x2 ≤ 1900

2x1 + 4x2 ≤ 1000

x1, x2 ≥ 0

-Find graphically the feasible region and the optimal solution.

Maximise 1170x1 + 1110x2

Subject to: 9x1 + 5x2 ≥ 500

7x1 + 9x2 ≥ 300

5x1 + 3x2 ≤ 1500

7x1 + 9x2 ≤ 1900 2x1 + 4x2 ≤ 1000 x1, x2 ≥ 0

-Find graphically the feasible region and the optimal solution.