MacDonald Products, Inc., of Clarkson, New York, has the option of
(a) proceeding immediately with production of a new top-of-the-line stereo TV that has just completed prototype testing or
(b) having the value analysis team complete a study.
If Tyrone Martin, VP for operations, proceeds with the existing prototype (option a), the firm can expect sales to be 120,000 units at $\$ 500$ each, with a probability of 0.56 and a 0.44 probability of 70,000 at $\$ 500$. If, however, he uses the value analysis team (option b), the firm expects sales of 85,000 units at $\$ 730$, with a probability of 0.65 and a 0.35 probability of 70,000 units at $\$ 730$. Value engineering, at a cost of $\$ 115,000$, is only used in option $\mathrm{b}$. Which option has the highest expected monetary value (EMV)?
The EMV for option a is $\$ \square$ and the EMV for option $\mathrm{b}$ is $\$$. Therefore, option $\nabla$ has the highest expected monetary value. (Enter your responses as integers.)
Answer
Compare the EMVs for options a and b to determine which option has the highest EMV: \(\boxed{\text{Option with highest EMV}}\)
Step 1 ：Calculate the Expected Monetary Value (EMV) for option a: \(EMV_a = (120,000 \text{ units} \times $500/\text{unit} \times 0.56) + (70,000 \text{ units} \times $500/\text{unit} \times 0.44)\)
Step 2 ：Calculate the Expected Monetary Value (EMV) for option b: \(EMV_b = [(85,000 \text{ units} \times $730/\text{unit} \times 0.65) + (70,000 \text{ units} \times $730/\text{unit} \times 0.35)] - $115,000\)
Step 3 ：Compare the EMVs for options a and b to determine which option has the highest EMV: \(\boxed{\text{Option with highest EMV}}\)
