Question

1.   A retired couple supplement their income by making fruit pies, which the sell to a nearby grocery store. The apple pies are sold for $1.50 and the grape pies for $1.20. The couple can sell all the pies they produce owing to their high quality. They use fresh ingredients. Flour and sugar are purchased once a month. For the month of September, they have 2,200 cups of sugar and 1,700 cups of flour. Each apple pie requires one and a half cups of sugar and three cups of flour, and each grape pie requires two cups of sugar and one and a half cups of flour. The couple working together can make an apple pie is five minutes and a grape pie in three minutes. The plan to work no more than 60 hours.

1. Summarize the data into a table as shown in Table B.1 on pg.701

Apple	Grape
X1	X2
3	1.5	<= 1700
1.5	2	<=2200
5	3	<=3600
1.5	1.2	MAX

2. Formulate the problem as a linear programming problem (Write it in its mathematical form).

  

Maximize Z = 1.5X1+1.2X2

Subject to:

                               3X1+1.5X2<=1700

                               1.5X1+2X2<=2200

                                  5X1+3X2<=3600

And

X1, X2>=0

Table B.1 Glickman Electronics Company Problem Data Example

	HOURS	REQUIRED TO	PRODUCE ONE UNIT
Department	X-PODS (X1)	BLUEBERRYS (X2)	AVAILABLE HOURS THIS WEEK
Electronic	4	3	240
Assembly	2	1	100
Profit per Unit	$7	$5

Answer 1

A retired couple problem

Below screenshot shows the approach for the solution using Excel -> Solver

Hence, the optimal solution for apple and grapes is below

Apple	Grape
27	1080

Maximum optimal profit is $1,336.

Glickman Electronics Company Problem Data

We can formulate the problem as below.

Maximize Z = 7X1+5X2

Subject to:

   4X1+3X2<=240

   2X1+1X2<=100   

And

X1, X2>=0

Below screenshot shows the approach for the solution using Excel -> Solver

Hence, the optimal solution is as below:

Department	X-PODS (X1)	BLUEBERRYS (X2)
Electronic	60	0
Assembly	0	100

Optimal maximum profit is $920.

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