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Feliz [49]
3 years ago
13

Autopitch devices are made for both​ major- and​ minor-league teams to help them improve their batting averages. When set at the

standard​ position, Autopitch can throw hardballs toward a batter at an average speed of 60 mph. To monitor these devices and to maintain the highest​ quality, Autopitch executives take samples of 10 devices at a time. The average range is 3 mph. Using this​ information, construct control limits for x overbar and R charts.

Business
1 answer:
aivan3 [116]3 years ago
5 0

Answer:

Control limits for x_bar are between 59.076 and 60.924

Control limits for R are between 0.669 and 5.331

Explanation:

Given data:

x_bar = 60 mph

n = 10

R = 3 mph

Step 1: Factors (see table attached)

At n = 10, factors for computing control charts limits are,

A2 = Mean factor = 0.308

D3 = Lower range = 0.223

D4 = Upper range = 1.777

Step 2: Control limits for x_bar

Lower Control limit:

LCL =  x_bar - A2*R = 60 - (0.308)(3) = 60 - 0.924 = 59.076

Upper Control limit:

UCL =  x-bar + A2*R = 60 + (0.308)(3) = 60 + 0.924 = 60.924

The control limits for x_bar are between 59.076 and 60.924

Step 3: Control limits for R

Lower Control limit:

LCL = D3*R = 0.223(3) = 0.669

Upper Control limit:

UCL = D4*R = 1.777(3) = 5.331

The control limits for R are between 0.669 and 5.331

Hope this helps!

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              Selling Price per unit Variable  cost per unit

Product  

Trunk Switch             $60.00               $28.00

Gas door             $75.00                $33.00

Glove Box            $40.00              $22.00

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The break-even point is the activity level where the total revenue of a business  exactly equals its cost. At the break-even point, <em>the total profit made will be zero</em>. This analysis enables a firm to determine ahead the number of units to must be produced, customers that must served in order to cover its fixed costs.

Calculation

A break-even point can be calculated as follows:

For single-product scenario:  

Break-even point (in units)= Total general fixed cost for the period/                (selling price-variable cost )

Multiple-products scenario= Total general fixed cost for the period/Average contribution per unit

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Variable cost                    (28)             (33)               (22)

Contribution per unit        32                42                  18

Cont. from a mix (sp×unit) 128              168                   18

Average cont. per mix = (128+168+18)/(4+4+1)= $34.89

Break-even point (in units)=  $18,840/$34.89

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Total units to be sold to break even is 540 units. This will be distributed across the three products using the sales mix as follows:

Trunk = 4/9× 540 units= 240 units

Gas = 4/9 × 540 = 240 units

Box = 1/9 *540 = 60 units

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