Dual Degree – Management UNPLecturerGesit Thabrani

Homework

Dual Degree – Management UNP

Operations Operations ResearchResearch

Task#1

Dual Degree – Management UNP

Problem #1Problem #1

Chad’s Pottery Barn has enough clay to make 24 small vases or 6 large vases. He has only enough of a special glazing compound to glaze 16 of the small vases or 8 of the large vases. Let X1 = the number of small vases and X2 = the number of large vases. The smaller vases sell for $3 each, and the larger vases would bring $9 each.

(a) Formulate the problem(b) Solve the problem graphically

Dual Degree – Management UNP

Problem #2Problem #2

The Munchies Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 milligrams of vitamin A and 12 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 8 milligrams of vitamin A and 1 milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 2 milligrams of B. An ounce of oats costs $0.05, and an ounce of rice costs $0.03.Formulate a linear programming model for this problem and find the optimal solution using graphical!

Dual Degree – Management UNP

PT CAT IS A SMALL FIRM THAT PRODUCES BOTH AA AND BB PAINT FROM TWO RAW MATERIALS, MATERIAL X AND MATERIAL Y

MAXIMUM DAILY AVAILABLE OF MATERIAL ARE 30 TONS MATERIAL X AND 40 TONS MATERIAL Y

TO MAKE 1 TON BB PAINT, THE FIRM USED 1 TON MATERIAL X AND 2 TON MATERIAL Y

TO MAKE 1 TON AA PAINT, THE FIRM USED 2 TONS MATERIAL X AND 1 TON MATERIAL Y

Problem #3Problem #3

Dual Degree – Management UNP

MARKET SURVEY INDICATES THAT :� THE DAILY DEMAND FOR AA PAINT CANNOT EXCEED THAT FOR BB PAINT BY MORE THAN 5 TON� ALSO, MAXIMUM DAILY DEMAND FOR AA PAINT IS 10 TONS

THE SELLING PRICE PER TON OF BB PAINT IS $3 AND SELLING PRICE PER TON OF AA PAINT IS $2

PT CAT WANTS TO DETERMINE THE OPTIMUM (BEST) PRODUCT MIX OF BB AND AA PAINTS THAT MAXIMIZES THE TOTAL DAILY INCOME

Problem #3Problem #3