Question

A quilter is making table runners and placemats. It takes her 12 minutes to make a table runner and 7.5 minutes to make a placemat. Each placemat uses 1.25 yards of fabric and each table runner uses 2/3 yard of fabric.

She has 31 hours available for making the table runners and placemats and has 237 yard of fabric on hand. She makes a profit of $2.50 on each table runner and $1.75 on each placemat. How many of each item should she make in order to maximize profit?

Use the solver to answer the following questions:

How many of each product should be sold to maximize profit?

What is the maximum profit that can be achieved?

What constraint(s) caused this solution to be the best possible?

Answer 1

Let the number of table runners = X

Let the number of placemats = Y

Z Max = 2.50X + 1.75

Subject to   ( Contraints)

2/3X + 1.25Y < / = 237 .............. (1)

12X + 7.5Y </= 1860    ................. (2)

18 * (1) ....... 12X + 22.5 Y = 4266

                     12X + 7.5 Y = 1860

15 Y = 2406

Y = 160.4 or 160 of Placemats

Substitute in any of the above equations ................ 12X + 7.5 (160.4) = 1860

12X = 657

X = 657 / 12 = 54.75 ........ or 54 Units of table runner

How many of each product should be sold to maximize profit?

Table runners = 54 Units and Placemat = 160 Units

What is the maximum profit that can be achieved?

Maximum profit = 2.5 * 54 + 1.75 * 160 = 415

What constraint(s) caused this solution to be the best possible?

Both fabric and working hours are the contraints used to get this best profit.