Question

1. 1. Yol's Brewery must decide how many barrels of the two types of beer (Yol's White and Yol's Red) to produce for its next shipment. It has limited supply of ingredients that are used in both products. Each barrel of Yol's White requires 20 lbs. of corn, 2 ozs. of hops, 10 lbs. of malt and yields €20 of profit. . Each barrel of Yol's Red requires 1 ozs. of hops, 30 lbs. of malt and yields €30 of profit. The company has 500 lbs. of corn, 60 ozs. of hops, 900 lbs. of malt at hand. Management wishes to determine the amount of White and Red to produce to maximize profits.
   2. A seamstress buys 90m of material to make dresses for both adults and children. She uses 1m of material for a child’s dress and 3m for an adult’s dress. It takes her 75 minutes to complete a child’s dress and 2 hours to complete an adult’s dress. She uses at most 80 hours to make dresses for children and dresses for adults. If she makes profit of ȼ7 on each child’s dress and ȼ14.50 on each adult’s dress, find how many of each kind of dress she should sew in order to make the greatest profit.
   3. A large school system wants to design a lunch menu containing two food items jollof rice and Fried rice. Each kilogram of Jollof rice supplies 1 units of protein, 2 units of carbohydrate and 1 unit of fat. Each kilogram of Fried rice supplies 1 unit of protein, 1 unit of carbohydrate and 1 units of fat. The two items together must provide at least 7 units of protein, at least 10 units of carbohydrate and not more than 8 units of fat per serving. If each kilogram of jollof rice cost $12000 and each kilogram of Fried rice cost $8000, determine how many kilograms of each item each serving should contain to meet the dietary requirement at the lowest cost.
   4. A manufacturer of animal feed makes two grades of food. Each bag of high grade feed contains 10kg of wheat brand and 5kg of maize, while each bag of low-grade feed contains 12kg of wheat brand and 3kg of maize. There are 1920kg of wheat brand and 780kg of maize currently available. The manufacture can make a profit of $12,000 on each bag of high grade and $10000 on each bag of the low-grade feed. Determine the number of bags of each grade to produce to maximize profit.
   5. A factory manufactures two products Coca Cola and Fanta, each requiring the use of three machines, M1, M2 and M3. M1 can be used as most 70 hours, M2 at most 40 hours and M3 at most 90 hours. Coca Cola requires 2 hours of M1, 1 hour on M2 and 1 hour on M3. Fanta requires 1 hours of M1, 1 hour on M2 and 3 hours on M3. If the profit is $400,000 per unit for product Coca Cola and $600,000 per unit for product Fanta, determine how many of each product to be manufactured to maximize profit.
   

Answer 1

1.

Corn (lbs)

Hops (ozs)

Malt (lbs)

Profit (euros)

Situation 1

If Produces 30 barrels of Yol's Red Beer then Yol's white beer cannotbe produced as Malt will all be consumed by Yol's Ref beer,

Profit = Euro 30 * 30 barrels = Euros 900

Situation 2

If Produces 25 barrels of Yol's White and 10 barrels of Yol's Red beer,

Profit = Euro 20 * 25 + euro 30 * 10 = Euros 800

Hence , to maximize profit company should produced only 30 barrels of Yol's red beer