Question

1. Andy Mendoza makes handcrafted dolls, which he sells at craft fairs. He is considering mass- producing the dolls to sell in stores. He estimates that the initial investment for plant and equipment will be $25,000, whereas labor, material, packaging, and shipping will be about $10 per doll. If the dolls are sold for $30 each, what sales volume is necessary for Andy to break even?
2. Andy Mendoza is concerned that the demand for his dolls will not exceed the break-even point. He believes he can reduce his initial investment by purchasing used sewing machines and fewer machines. This will reduce his initial investment from $25,000 to $17,000. However, it will require his employees to work slowly and perform more operations by hand, thus increasing variable cost from 10 to $14 per doll. Will these changes reduce the break-even point?.

3. XYZ company is manufacturing two products A and B. Production is limited to 80 units of product A and 60 units of product B due to limited supply of raw material. Production of each of these products requires 5 units and 6 units of electronic components respectively. The electronic components are supplied by another manufacturer and the supply is limited to 600 units per day. The company has 160 employees, i.e., the labor supply amounting to 160 man days. The production of one unit of product A requires one man-day of labor the production of one unit of product B requires two man-days of labor. Each unit of these products is sold in the market at a profit of OR 50 and OR 80 respectively. Determine how many units of each product the company should produce to maximize profit. A) Formulate this linear programing problem. B) Find the optimal solution by graphical method and communicate your decision.

Answer 1

Question 1

Scenario 1- Fixed cost = $25000 Variable cost= $10 Price = $30

To breakevem $30x = $10x + 25000 where x is number of dolls sol

20x = 25000 . X = 1250 units

Scenario 2

Fixed cost = $17000 VC=$14 Price =$30

To breakeven 30x = 14x + 17000

16x= 17000 x = 1062.5

Question 2

Let number of units produced of A = a

Let number of units produced of B = b

Maximize = 50a + 80b

Condition 1 a <=80

Condition 2 b <=60

Condition 2 5a + 6b <=600

Condition 3 a + 2b <= 160

Solving for Condition 1 a=80; solving for condition 2 b=60 (Draw lines)

Solving for Condition 3 to get coordinates for graph 5a+6b=600; if a =0 then b = 100 and if b=0 a= 120

Solving for Condition 4 to gte coordinates for graph a=0 then b =80 and if b=0 a= 160

Solve for equations :

Multiply Condition 4 by 5

Condition 4 *5 5a +10b = 800

Less Condition 3 5a+ 6b = 600

4b = 200

b = 50 Putting value of B in Condition 3

5a= 600 - 300

a = 60

0 20 40 60 80 100 120

Answer 2

By given data of old BEP & new BEP

Breakeven point = Fixed cost / (Selling price – variable cost)

Old breakeven point = 25000/(30-10) = 1250

New breakeven point = 17000/(30-14) =1062.5 or 1063 units (rounding up)

This means the breakeven point will reduce by 1250-1063 = 187