A friend promises to call you at home sometime between 3 P.M. and 4 P.M. At 2:45 P.M. you must leave your house unexpectedly for half an hour. What is the probability you miss the first call?

Write the problem in normal form and solve it by the simplex method, assuming all the $x_j$ to be nonnegative.

Maximize $z=2 x_1+x_2+3 x_3$ subject to $4 x_1+3 x_2+6 x_3 \leqq 12$.

Compare the areas of two sectors if they have the same central angle, but the radius of one is twice as long as the radius of the other.

Lazer Technologies Inc. (LTI) has produced a total of $20$ high-power laser systems that could be used to destroy any approaching enemy missiles or aircraft. The $20$ units have been produced, funded in part as private research within the research and development arm of LTI, but the bulk of the funding came from a contract with the U.S. Department of Defense (DoD).

Testing of the laser units has shown that they are effective defense weapons, and if redesigned to add portability and easier field maintenance, the units could be truck-mounted. The DoD has asked LTI to submit a bid for $100$ units. The $20$ units that LTI has built so far cost the following amounts and are listed in the order in which they were produced.

$$\begin{array}{cccc} \text { Unit Number } & \text { Cost }(\$ \text { millions) } & \text { Unit Number } & \text{ Cost (\$ millions) } \\ 1 & \$ 12 & 11 & 3.9 \\ 2 & 10 & 12 & 3.5 \\ 3 & 6 & 13 & 3.0 \\ 4 & 6.5 & 14 & 2.8 \\ 5 & 5.8 & 15 & 2.7 \\ 6 & 6 & 16 & 2.7 \\ 7 & 5 & 17 & 2.3 \\ 8 & 3.6 & 18 & 3.0 \\ 9 & 3.6 & 19 & 2.9 \end{array}$$

a. Based on past experience, what is the learning rate?

b. What bid should LTI submit for the total order of $100$ units, assuming that learning continues?

c. What is the cost expected to be for the last unit under the learning rate you estimated ?

Maximize f=2x1+3x2+2x3, x1≥0, x2≥0, x3≥0, x1+2x2-4x3≤2, x1+2x2+2x3≤5.

Olive Construction Company is determining whether it should submit a bid for a new shopping center. In the past, Olive's main competitor, Base Construction Company, has submitted bids $70 \%$ of the time. If Base Construction Company does not bid on a job, the probability that Olive Construction Company will get the job is 0.50. If Base Construction Company bids on a job, the probability that Olive Construction Company will get the job is 0.25 .

If Olive Construction Company gets the job, what is the probability that Base Construction Company did not bid?

A contractor submits a bid on a project for which more research and development work needs to be done. It is estimated that the total cost of satisfying the project specifications will be $20 million plus the cost of the further research and development work. The contractor views the cost of this additional work as a random variable with a mean of$4 million and a standard deviation of $1 million. The contractor wishes to submit a bid such that his expected profit will be 10% of his expected costs. What should be the bid? If this bid is accepted, what will be the standard deviation of the profit made by the project?

Olive Construction Company is determining whether it should submit a bid for a new shopping center. In the past, Olive's main competitor, Base Construction Company, has submitted bids $70 \%$ of the time. If Base Construction Company does not bid on a job, the probability that Olive Construction Company will get the job is 0.50. If Base Construction Company bids on a job, the probability that Olive Construction Company will get the job is 0.25 .

What is the probability that Olive Construction Company will get the job?

Lazer Technologies Inc. (LTI) has produced a total of 20 high-power laser systems that could be used to destroy any approaching enemy missiles or aircraft. The 20 units have been produced, funded in part as private research within the research and development arm of LTI, but the bulk of the funding came from a contract with the U.S. Department of Defense (DoD). Testing of the laser units has shown that they are effective defense weapons, and through redesign to add portability and easier field maintenance, the units could be truck-mounted. DoD has asked LTI to submit a bid for 100 units. The 20 units that LTI has built so far cost the following amounts and are listed in the order in which they were produced. What bid should LTI submit for the total order of 100 units, assuming that learning continues?

Lazer Technologies Inc. (LTI) has produced a total of 20 high-power laser systems that could be used to destroy any approaching enemy missiles or aircraft. The 20 units have been produced, funded in part as private research within the research and development arm of LTI, but the bulk of the funding came from a contract with the U.S. Department of Defense (DoD). Testing of the laser units has shown that they are effective defense weapons, and through redesign to add portability and easier field maintenance, the units could be truck-mounted. DoD has asked LTI to submit a bid for 100 units. The 20 units that LTI has built so far cost the following amounts and are listed in the order in which they were produced. What is the cost expected to be for the last unit under the learning rate you estimated?

Olive Construction Company is determining whether it should submit a bid for a new shopping center. In the past, Olive's main competitor, Base Construction Company, has submitted bids 70% of the time. If B ase Construction Company does not bid on a job, the probability that Olive Construction Company will get the job is 0.50. If B ase Construction Company bids on a job, the probability that Olive Construction Company will get the job is 0.25.

a. If Olive Construction Company gets the job, what is the probability that Base Construction Company did not bid?

b. What is the probability that Olive Construction Company will get the job?

Lazer Technologies Inc. (LTI) has produced a total of 20 high-power laser systems that could be used to destroy any approaching enemy missiles or aircraft. The 20 units have been produced, funded in part as private research within the research and development arm of LTI, but the bulk of the funding came from a contract with the U.S. Department of Defense (DoD). Testing of the laser units has shown that they are effective defense weapons, and through redesign to add portability and easier field maintenance, the units could be truck-mounted. DoD has asked LTI to submit a bid for 100 units. The 20 units that LTI has built so far cost the following amounts and are listed in the order in which they were produced. Based on past experience, what is the learning rate?

Changing cash conversion cycle Camp Manufacturing turns over its inventory five times each year, has an average payment period of 35 days, and has an average collection period of 60 days. The firm has annual sales of $3.5 million and cost of goods sold of$2.4 million. a. Calculate the firm’s operating cycle and cash conversion cycle.

High-power lasers in factories are used to cut through cloth and metal. One such laser has a beam diameter of 1.00 mm and generates an electric field having an amplitude of 0.700 MV/m at the target. Find (a) the amplitude of the magnetic field produced, (b) the intensity of the laser, and (c) the power delivered by the laser. A laser cutting device mounted on a robot arm is being used to cut through a metallic plate.