1.Ruben intends to invest an amount of Php 50,000 in either a trust fund or a time deposit or both ventures. The trust fund pays 8% per annum while the time deposit pays 9% per annum. Because the trust fund is riskier than the time deposit, he does not want to have some money readily available if needed, so he intends to put at least Php 10,000 in time deposit and Php 30,000 in trust fund. How much should he allot to each investment to maximize his returns?   2.MMW company manufactures two alloy products: round bar and flat disk. Each unit of round bar contains 2 kilograms of aluminum and 1 kilogram of steel. Each unit of flat disk contains 14 kilograms of aluminum and 2 kilograms of steel. MMW company has an available supply of 70 kilograms of aluminum and 20 kilograms of steel. MMW company makes a profit of Php 20.00 on each unit of round bar and Php 50.00 on each unit of flat disk. Determine the number of units of round bar and flat disk it must manufacture in order to maximize its profit.   3.Katya Publishing company is planning to bind a mathematics book in two different bindings: paperback and hardcover. Each book goes to two processes, sewing and gluing. The following table give information on this problem: Paperback Gluing Sewing time 3 minutes 3 minutes Gluing time 5 minutes 10 minutes Profit/book Php 10.00 Php 15.00 How many books of each binding should Katya Publishing make to maximize profit if each day the available sewing time is 6 hours and the available gluing time is 10 hours?    4. A diabetic patient needs at least 40 units of Vitamin A, at least 30 units of Vitamin C and at least 30 units of Vitamin E each day. Each brand X multivitamin capsule contains 4 units of A, 6 units of C and 2 units of E; each brand Y capsule contains 5 units of A, 3 units of C and 5 units of E. If each brand X capsule costs Php 6.00 and each brand Y costs Php 9.00, how many capsules should the patient take each day to minimize the cost?    5.ROA Agri Feeds Corporation produces specially blended feed supplements. It has an order of 400 kilograms of the mixture. This consists of two ingredients: a source of protein and a source of carbohydrates. The first ingredient costs P6.00 a kg. The second ingredient costs

1.Ruben intends to invest an amount of Php 50,000 in either a trust fund or a time deposit or both
ventures. The trust fund pays 8% per annum while the time deposit pays 9% per annum. Because the
trust fund is riskier than the time deposit, he does not want to have some money readily available if
needed, so he intends to put at least Php 10,000 in time deposit and Php 30,000 in trust fund. How
much should he allot to each investment to maximize his returns?

2.MMW company manufactures two alloy products: round bar and flat disk. Each unit of round bar
contains 2 kilograms of aluminum and 1 kilogram of steel. Each unit of flat disk contains 14
kilograms of aluminum and 2 kilograms of steel. MMW company has an available supply of 70
kilograms of aluminum and 20 kilograms of steel. MMW company makes a profit of Php 20.00 on
each unit of round bar and Php 50.00 on each unit of flat disk. Determine the number of units of round
bar and flat disk it must manufacture in order to maximize its profit.

3.Katya Publishing company is planning to bind a mathematics book in two different bindings:
paperback and hardcover. Each book goes to two processes, sewing and gluing. The following table
give information on this problem:
Paperback Gluing
Sewing time 3 minutes 3 minutes
Gluing time 5 minutes 10 minutes
Profit/book Php 10.00 Php 15.00

How many books of each binding should Katya Publishing make to maximize profit if each day the
available sewing time is 6 hours and the available gluing time is 10 hours? 

4. A diabetic patient needs at least 40 units of Vitamin A, at least 30 units of Vitamin C and at least 30
units of Vitamin E each day. Each brand X multivitamin capsule contains 4 units of A, 6 units of C
and 2 units of E; each brand Y capsule contains 5 units of A, 3 units of C and 5 units of E. If each
brand X capsule costs Php 6.00 and each brand Y costs Php 9.00, how many capsules should the
patient take each day to minimize the cost? 

5.ROA Agri Feeds Corporation produces specially blended feed supplements. It has an order of
400 kilograms of the mixture. This consists of two ingredients: a source of protein and a
source of carbohydrates. The first ingredient costs P6.00 a kg. The second ingredient costs
P16.00 a kg. The mixture cannot be more than 150 kilograms and it must have at least 200
kilograms of second ingredient. The company’s problem is to determine how much of each
ingredient to use to minimize cost but satisfy the requirements.