# 1. formulate the following problem as a linear program but do not solve.

My diet requires that all the food i eat come from one of the four "basic food group" ( chocolate cake, ice cream, soda, and cheese cake). At present , the following four foods are available for consumption: brownies, chocolate ice cream, cola, and pineapple cheesecake. Each brownie costs 50c, each scoop of chocolate ice cream costs 20c , each bottle of cola costs 30c , and each piece of pineapple cheesecake costs 80c.Each day i must ingest at least 500 calories , 6oz of chocolate, 10oz of sugar , and 8oz of fat. The nutritional content per unit of each food is shown in the following table .

formulate a linear programming model that can be used to satify my daily nutritional requirements at minimum cost

TYPE OF FOOD CALORIE CHOCOLATE(ounces) SUGAR(ounces) FAT(ounces)

Brownie 400 3 2 2

Chocolate ice cream

( 1 scoop) 200 2 2 4

Cola (1 bottle) 150 0 4 1

Pineapple cheesecake

(1 piece) 500 0 4 5

# 2. Formulate but do not solve the following as a linear program.

During each 4-hour period, the smalltown police force requires the following number of on-duty police officers:

12midnight to 4 A.M.-8;4 to 8 A.M.-7;8 A.M to 12 Noon-6; 12 noon to 4 P.M.-6;4 p.m. to 8 P.M.-5; 8 P.M. to 12 midnight-4. Each police officer works two consecutive 4-hour shifts. Formulate an linear program that can be used to minimize the number of police officers needed to meet Smalltown's daily requirements.

# 3. Formulate but do not solve the following problem as a linear program.

O.J Juice company sells bags of oramges and cartons of orange juice. O.J grades oranges on a scale of 1 (poor) to 10 (excellent). O.J now has on hand 100,000 lb of grade 9 oranges and 120,000 lb of grade 6 oranges. The average quality of oranges sold in bags must be at least 7, and the average quality of oranges used to produce orange juice must be at least 8. Each pound of oranges that is used for juice yields a revenue of $1.50 and incurs a variable cost ( consisting of labor costs, variable overhead costs, inventory costs , and so on) of $ 1.05. EACH pound of oranges sold in bags yields a revenue of 50c and incurs a variable costs of 20c. formulate an linear program to help O.J maximize profit.

# 4. formulate but do not solve the following problem ads a linear program.

sunco oil produces oil at two wells. Well 1 can produce as many as 150,000 barrels per day , and Well 2 can produce as many as 200,000 barrels per day . It is possible to ship oil directly from the wells to Sunco's customers in Los Angeles and New York. Alternatively , Sunco could transport oil to the ports of mobile and Galveston and then ship it by tanker to New York or Los Angeles. Los Angeles requires 160,000 barrels per day, and New York requires 140,000 barrels per day . The costs of shipping 1000 barrels between two points are shown in the following table . formulate a transshipment model that could be used to minimize the transport costs in meeting the oil demands of Los Angeles and New York.

TO($)

FROM WELL 1 WELL 2 MOBILE GALVESTON N.Y L. A

WELL 1 0 - 10 13 25 28

WELL 2 - 0 15 12 26 25

MOBILE - - 0 6 16 17

GALVESTON - - 6 0 14 16

N.Y. - - - - 0 15

L.A. - - - - 15 0

COURSE : SUPPLY CHAIN MANAGEMENT

BOOK : Business Analytics The art of modeling with spread sheet fifth edition Powell and Baker chapter 9