1. An engineering manufacturing company has established that the relationship between the quantity sold per month (D) and the sales (6780-5p)² price (p) for one of its products is approximately, units. The fixed cost is $1000 per month and the unit variable cost is $550 per unit produced. a. What is the maximum total revenue per month? Prove it is a maximum. b. What is the maximum profit per month? Prove it is maximum.

1.5 A physician has ordered 37.5 mg of a particular drug over 15 minutes. If the drug was available as 2.5 mg/mL of solution, how many mL would you need to give cvery 15 seconds? 15 sec

A new generator has been installed. There will be no maintenance cost until the end of the sixth year when P500 will be spent at the end of each successive year until the fourteenth year when the generator will be scrapped. How much money should be set aside now to be able to sustain these maintenance charges at 6% annually? Please show the cash flow diagram. Thank you very much

Q5. An established company has decided to add a new product to its line. It will buy the product from a manufacturing concern, package it, and sell it to a number of distributors that have been selected on a geographical basis. Market research has already indicated the volume expected and the size of sales force required. The steps shown in the following table are to be planned. Activity Description Predecessor Activity Duration (days) A B C D E F LL C A B C A E E E H,L K 14 4 2 1 2 3 2 4 3 12 4 2 2 G H 1 J K L M H,L (a) Draw an arrow diagram for the project. (b) Indicate the criticla path. (c) For each non-critical activity, find the total and free float. D,F,G J

Q1: Two manufacturing plants produce similar parts. Plant 1 produces 1,000 parts, 100 of which are defective.Plant 2 produces 2,000 parts, 150 of which are defective. A part is selected at random and found to be defective. What is the probability that it came from plant 1 ?

A toy factory is planning to make an additional item, which would be processed in 4 departments. The company is proposing to produce 600,000 units per year, working 250 days per year. The estimates of times made by an industrial engineer are in the table:                                  Departments Times   1   2   3    4 Average processing time (second/part) 8  13 10 50 Average maintenance, time/day (minutes) 20 30 20 15 Average daily setup, time (minutes) 20 15 30 20 Average bookkeeping, time/day (minutes) 10 8 12 5 Machine adjustment, time/day (minutes) 15 10 15 15 Defective items, (% of production) 5  6   4   4 The parts are produced within the departments in a sequential manner (from department 1 to 2 to 3 to 4).    Determine the efficiency of each departmental operation if only one shift is operated between 7:30 am-4:30 pm, with a 40 minute lunchbreak and two 10 minute coffee breaks.

In machine design we usually compare the equivalent stress of the component with the: a) Allowable stress b) Machine stress c) Force d) Moment e) Torque

10. In the figure below, h, = 1.20 m, h, = 0.80 m, and the length along the wire from A to C is 6.00 m. A 3.00-gram bead starting from rest at A slides along the wire to point C and stops. How large an average friction force opposed its motion? h2 B A) 1.45 x 103 N B) 3.12 x 10 N C) 2.55 x 103 N D) 1.96 x 10³ N

See image.

How did they get these answers for b) and c) ?