A firm making production plans believes there is a 30% probability the price will be $10,a 50% probability the price will be $15,and a 20% probability the price will be $20.The manager must decide whether to produce 6,000 units of output A),8,000 units B)or 10,000 units C).The following table shows 9 possible outcomes depending on the output chosen and the actual price. What is the variance if 6,000 units are produced?

Question

A firm making production plans believes there is a 30% probability the price will be $10,a 50% probability the price will be $15,and a 20% probability the price will be $20.The manager must decide whether to produce 6,000 units of output A),8,000 units B)or 10,000 units C).The following table shows 9 possible outcomes depending on the output chosen and the actual price.  What is the variance if 6,000 units are produced?

Quizplus · Accepted Answer

To calculate the variance, we need to first find the expected value for each output decision. 
For 6,000 units: 
Expected value = (0.30 x 10) + (0.50 x 15) + (0.20 x 20) = 13.5 
Variance = [(10-13.5)^2 x 0.30] + [(15-13.5)^2 x 0.50] + [(20-13.5)^2 x 0.20] 
= 176,400

For 8,000 units: 
Expected value = (0.30 x 10) + (0.50 x 15) + (0.20 x 20) = 13.5 
Variance = [(10-13.5)^2 x 0.30] + [(15-13.5)^2 x 0.50] + [(20-13.5)^2 x 0.20] 
= 122,500

For 10,000 units: 
Expected value = (0.30 x 10) + (0.50 x 15) + (0.20 x 20) = 13.5 
Variance = [(10-13.5)^2 x 0.30] + [(15-13.5)^2 x 0.50] + [(20-13.5)^2 x 0.20] 
= 202,500

Therefore, the best choice is to produce 6,000 units as it has the lowest variance.

A Firm Making Production Plans Believes There Is a 30