Valu-Com Electronics manufactures five different models of telecommunications interface cards for PCs and laptops. As summarized in the following table, each of these devices requires differing amounts of printed circuit board, resistors, memory chips, and assembly. Hyper Link Fast Link Speed Link Micro Link Ether Link
Printed Circuit Board (square inches) 20 15 10 8 5
Resistors 28 24 18 12 16
Memory Chips 8 8 4 4 6
Assembly Labor (in hours) 0.75 0.6 0.5 0.65 1

The unit wholesale price and manufacturing cost for each model are as follows:
Per unit Revenues and Costs
Hyper Link Fast Link Speed Link Micro Link Ether Link
Wholesale Price $189 $149 $129 $169 $139
Manufacturing Cos $136 $101 $96 $137 $101

In its next production period, Valu-Com has 80,000 square inches of PC board, 100,000 resistors, 30,000 memory chips, and 5,000 hours of assembly time available. The company can sell all the product it can manufacture, but the marketing department wants to be sure the company produces at least 500 units of each product and at least twice as many FastLink cards as HyperLink cards while maximizing profit.

a. Formulate an LP model for this problem.
b. Create a spreadsheet model for this problem, and solve it using Solver.
c. What is the optimal solution?
d. Could Valu-Com make more money if it schedules assembly workers to work overtime?

How is the number of vertices for a prism related to the name of the prism

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.

If the ratio of sum of the first m and n terms of an ap is m2 : n2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1).