Finite Review – Chapter 3 NAME ______

Inequalities and Linear Programming DATE ______BLOCK ___

Graph each of the following.

1.

Graph each linear system.

3.

Identify Corner Points:

2.

4.

Identify Corner Points:

5.

Find the vertices of the bounded

region by the elimination method:

6. Explain in words the difference between an unbounded and bounded region and what the objective is for each type of graph.

For the following Linear Programming in problems #7-9 SET-UP only (Steps 1-3)!

7. The Humidor blends regular coffee, High Mountain coffee, and chocolate to obtain four kinds of coffee: Early Riser, Coffee Time, After Dinner, and Deluxe. The blends and profit for each blend are given in the chart on pg 255 #4. The shop has 260 pounds of regular coffee, 90 pounds of High Mountain coffee, and 20 pounds of chocolate. How many pounds of each blend should be produced to maximize profit.

8. Ms. Gacki plans to open the Common Grounds Coffee House. Initially, she plans to offer an upscale regular coffee and a prized gourmet coffee. Her supplier requires a minimum of 60 pounds per order. The regular coffee costs $4.35 per pound and the gourmet coffee $6.40 per pound. Ms. Gacki has been told to order at least 25 pounds of regular coffee and at least 45 pounds of gourmet coffee. How much of each kind should Ms. Gacki order to minimize her coffee costs?

9. A freight company has two sizes of trucks for hauling freight. Type A has a capacity of 8 tons, and type B has a capacity for 11 tons. An order is received to haul 230 tons of freight to Columbus and 145 tons to Anderson. The cost of making the trip is the following:

Hauling Cost per Trip

Truck / Columbus / Anderson
A / $600 / $450
B / $720 / $525

Find the number of trips each type truck must make to each city to fill the order and to minimize the hauling costs.

Solve each of the following Linear Programming problems. Show all steps!

10. The maximum production of a soft-drink bottling company is 5000 cartons per day. The company produces two kinds of soft-drinks, regular and diet. It costs $1.00 to produce each carton of regular and $1.20 to produce each carton of diet. The daily operating budget is $5400. The profit is $.15 per carton on regular and $.17 per carton on diet drinks. How much of each type of drink is produced to obtain the maximum profit?

11. Freezer Linear Programming Problem – Show all 8 steps!!!

An appliance store manager is ordering chest and upright freezers. One chest freezer costs $250 and delivers a $40 profit. One upright freezer costs $400 and delivers a $60 profit. Based on previous sales, the manager expects to sell at least 100 freezers. Total profit must be at least $4800. Find the least number of each type of freezer the manager should order to minimize costs.