Question

1) You plan a meal with the following ingredients and requirements:

	bread	potatoes	meat	beans	eggs	butter	requirement
units	lb	lb	oz	lb	number	oz
cost	$1.89	$0.75	$0.48	$2.29	$0.15	$2.85
calaries	280	250	43	78	160	300	2200	at least
vitamin A	5	15	37	20	12	0	300	at least
vitamin c	0	70	0	50	0	0	60	at least
protein	3	5	40	12	10	0	80	at least
fat	8	2	25	3	18	30	50	at least

a. Find the cheapest meal that satisfies all the requirements. What are the ingredients and what is the total cost.

b. Find the integer solution to this problem.

c. Can you use these results?

2) You have three plants that produce a certain type of boats. The capacity for next month is 38 in San Diego, 45 in Santa

Ana, and 58 in San Jose. Production cost per boat is $1,065 in San Diego, $1,005 in Santa Ana, and $975 in San Jose.

Demand for next month is 42 in Newport Beach, 33 in Long Beach, 14 in Ventura, 10 in San Luis Obispo, and 22 in San

Francisco. The shipping costs per boat are summarized in the following table:

	Shipping	Cost	to:
From	NB	LB	VEN	SLO	SF
SD	$200	$220	$280	$350	$400
SA	$125	$125	$280	$350	$400
SJ	$390	$365	$300	$250	$100

Develop a production and shipping schedule that minimizes the total cost of production and shipping while satisfying all

the demand.

3) You own a wheat warehouse with a capacity of 20 thousand bushels. At the beginning of month 1, you have 6 thousand

bushels of wheat. Each month, wheat can be bought and sold at the prices per one thousand bushels shown in the table

below.

The sequence of events during each month is as follows:

You observe your initial stock of wheat.

You can sell any amount of wheat up to your initial stock at the current month’s selling price.

You can buy as much wheat as you want, subject to the warehouse size limitation.

Determine how to maximize the profit earned over the next 10 months by finding the quantities to sell and buy each

month. What is your profit?

	selling price	purchase price
month 1	$3	$8
month 2	$6	$8
month 3	$7	$2
month 4	$1	$3
month 5	$4	$4
month 6	$5	$3
month 7	$5	$3
month 8	$1	$2
month 9	$3	$5
month 10	$2	$5

Answer 1

1.

Apply formulas as shown below

The solver parameters are shown below

The result is shown below. It is highlighted in yellow.

Ideal approach is to consumer 1lb of potatoes and 24 eggs. The cost will be $4.35