1.- Solve: 3x + 5y < 2(x+2)

a)

b)

c)

d) None of them

2.- Solve: y ≥ 3x + 6

3.- Solve:

4.- Solve:

d) No solution

5.- Solve:

6.- A farmer can plant up to 8 acres of land with wheat and barley. He can earn 5000 € for every acre he plants with wheat and 3000 € for every acre he plants with barley. His use of a necessary pesticide is limited by federal regulations to 10 gallons for his entire 8 acres. Wheat requires 2 gallons of pesticide for every acre planted and barley requires just 1 gallon per acre. What is the maximum profit he can make?

a) 24000 €

b) 25000 €

c) 28000 €

d) 30000 €

7.- A painter has exactly 32 units of yellow dye and 54 units of green dye. He plans to mix as many gallons as possible of color A and color B. Each gallon of color A requires 4 units of yellow dye and 1 unit of green dye. Each gallon of color B requires 1 unit of yellow dye and 6 units of green dye. Find the maximum number of gallons he can mix.

a) 6 galons of color A and 8 galons of color B

b) 0 galons of color A and 9 galons of color B

c) 8 galons of color A and 0 galons of color B

d) 8 galons of color A and 6 galons of color B

8.- A garden shop wishes to prepare a supply of special fertilizer at a minimal cost by mixing two fertilizers, A and B. The mixture must contain:at least 45 units of phosphate, at least 36 units of nitrate and at least 40 units of ammonium. Fertilizer A costs the shop 0.97 € per pound. Fertilizer B costs the shop 1.89 € per pound. Fertilizer A contains 5 units of phosphate and 2 units of nitrate and 2 units of ammonium and fertilizer B contains 3 units of phosphate and 3 units of nitrate and 5 units of ammonium. How many pounds of each fertilizer should the shop use in order to minimize their cost?

a) 20 pounds of fertilizer A and 0 pounds of fertilizer B

b) 0 pounds of fertilizer A and 15 pounds of fertilizer B

c) 3 pounds of fertilizer A and 10 pounds of fertilizer B

d) 15 pounds of fertilizer A and 2 pounds of fertilizer B

9.- A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 1000 scientific and 800 graphing calculators each month. Because of limitations on production capacity, no more than 2000 scientific and 1700 graphing calculators can be made monthly. To satisfy a supplying contract, a total of at least 2000 calculators must be supplied each month. If each scientific calculator sold results in 120 € profit and each graphing calculator sold produces a 150 € profit, how many of each type of calculators should be made monthly to maximize the net profit.

a) The company should manufacture 1200 scientific calculators and 800 graphing calculators

b) The company should manufacture 1000 scientific calculators and 1000 graphing calculators

c) The company should manufacture 1000 scientific calculators and 1700 graphing calculators

d) The company should manufacture 2000 scientific calculators and 1700 graphing calculators

10.- We need to buy some cabinets for a room. There are two types of cabinets that you have liked in the market, say X and Y. Each unit of cabinet X costs you 15000 € and requires 6 square feet of floor space, and holds 8 cubic feet of files. On the other hand each unit of cabinet Y costs 12000 €, requires 8 square feet of floor space and holds 12 cubic feet of files. You have been given 140000 € for this purchase, though you may not spend all. The office has room for no more than 72 square feet of cabinets. How many of each model must you buy in order to maximize the storage volume?

a) 5 type X cabinets and 5 type Y cabinets

b) 9 type Y cabinets

c) 3 type X cabinets and 6 type Y cabinets

d) 9 type X cabinets

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