A monthly overhead of a manufacturer of a certain commodity is P6000 and the cost of material is P1.0 per unit. If not more than 4500 units are manufactured per month, labor cost is P0.40 per unit, but for each unit over 4500, the manufacturer must pay P0.60 for labor per unit. The manufacturer can sell 4000 units per month at P7.0 per unit and estimates that monthly sales will rise by 100 for each P0.10 reduction in price. Find the number of units that should be produced each month for maximum profit.

A rectangular field has an area of 10,000 sq m. What is the least amount of fencing meters to enclose it?

The hypotenuse of a right triangle is 20 cm. What is the max possible area of the triangle in sq cm?

If the hypotenuse of a right triangle is known, what is the relation of the base and the altitude of the right triangle when its area is maximum?

A wall 2.245 m high is 2 m away from a bldg. Find the shortest ladder that can reach the building with one end resting on the ground outside the wall.

The total cost of producing and marketing x units of a certain commodity is given as C = (80000x – 400x2 + x3)/40000. For what number x is the average cost a minimum?

The fixed monthly cost for operating a manufacturing plant that makes transformers is P8000 and there are direct costs of P110 for each unit produced. The manufacturer estimates that 100 units per month can be sold if the unit price is P250 and that sales will in crease by 20 units for each P10 decrease in price. Compute the number of units that must be sold per month to maximize the profit. Compute the unit price.

ABC company manufactures computer spare parts. With its present machines, it has an output of 500 units annually. With the addition of the new machines the company could boosts its yearly production to 750 units. If it produces x parts it can set a price of P = 200 – 0.15x pesos per unit and will have a total yearly cost of C = 6000 + 6x – 0.003x in pesos. What production level maximizes total yearly profit?

In manufacturing and selling x units of a certain commodity, the selling price per unit is P = 5 – 0.002x and the production cost in pesos is C = 3 + 1.10x. Determine the production level that will produce the max profit and what would this profit be?

The highway department is planning to build a picnic area for motorist along a major highway. It is to be rectangular with an area of 5000 sq m is to be fenced off on the three sides not adjacent to the highway. What is the least amount of fencing that ill be needed to complete the job?

f the sum of the two numbers is 4, find the minimum value of the um of their cubes.

A manufacturer estimates that the cost of production of x units of a certain item is C = 40x – 0.02x2 – 600. How many units should be produced for minimum cost?

A piece of plywood for a billboard has an area of 24 sq ft. The margins at the top and bottom are 9 inches and at the sides are 6 in. Determine the size of plywood for maximum dimensions of the painted area.

A rectangular corral is to be built with a required area. If an existing fence is to be used as one of the sides, determine the relation of the width and the length which would cost the least.

A printed page must contain 60 sq m of printed material. There are to be margins of 5 cm on either side and margins of 3 cm on top and bottom. How long should the printed lines be in order to minimize the amount of paper used?

The stiffness of a rectangular beam is proportional to the breadth and the cube of the depth. Find the shape of the stiffest beam that can be cut from a log of given size.

What is the maximum length of the perimeter if the hypotenuse of a right triangle is 5m long?

A plate in the form of parabolic segment is 12 m in height and 4 m deep and is partly submerged in water so that its axis is parallel to end 3 m below the water surface. Find the force acting on the plate.

Find the force on one face of a right triangle of sides 4 m, and altitude of 3 m. The altitude is submerged vertically with the 4 m side in the surface.

A rectangular plate is 4 feet long and 2 feet wide. It is submerged vertically in water with the upper 4 feet parallel and to 3 feet below the surface. Find the magnitude of the resultant force against one side of the plate.

Evaluate the integral of cos5 φ dφ if the lower limit is 0 and the upper limit is π/2.

What is the integral of sin6 (φ)cos4 (φ) dφ if the upper limit is π/2 and lower limit is 0?

Find the moment of inertia with respect to x-axis of the area bounded by the parabola y2 = 4x and the line x = 1.

Find the moment of inertia of the area bounded by the curve y2 = 4x, the line y = 2 and the y-axis on the first quadrant with respect to y-axis.

A simple beam having a span of 6m has a weight of 20 kN/m. It carries a concentrated load of 20 kN at the left end and 40 kN at 2m from the right end of the beam. If it is supported at 2 m from the left end and the right end, compute the reaction at the right end of the beam.

A wire connects a middle of links AC and AB compute the tension in the wire if AC carries a uniform load of 600 N/m. AC is 4.5 m long and BC is 7.5 m. point A is hinged on the wall and joint C is also hinged connecting the links AC and CB. AC is horizontal while B is supported by roller acting on the wall AB.

An airtight closed box of weight P is suspended from a spring balance. A bird of weight W is place on the floor of the bow, and the balance reads W + P. If the bird flies without accelerating. What is the balance reading?

A tripod whose legs are each 4 meters long supports a load of 1000 kg. the feet of the tripod are at the vertices of a horizontal equilateral triangle whose side are 3.5 meters. Determine the load of each leg.

A uniform square table top ABCD having sides 4m long is supported by three vertical supports at A, E and F, E is midway n the side BC and F is 1m from D along the side DC. Determine the share of load in percent carried by supports at A, E and F.

A horizontal Circular platform of radius R is supported at three points A, B and C on its circumference. A and B are 90 degrees apart and C is 120 degrees from A. The platform carries a vertical load of 400 kN at its center and 100 kN at a point d on the circumference diametrically opposite A. Compute the reaction at C.

A ladder 4m long having a mass of 15 kg is resting against a floor and an wall for which the coefficients of static friction are 0.30 for the floor to which a man having a mass of 70 kg can climb without causing the plank to slip if the plank makes an angle of 40 degrees with the horizontal.

A homogenous block having dimension of 4 cm by 8 cm is resting on an inclined plane making an angle of θ with the horizontal. The block has a weight of 20 kN. If the coefficient of friction between the block and the inclined plane is 0.55, find the value of θ before the block starts to move. The 8cm side is perpendicular to the inclined plane.

A block having a mass of 250 kg is placed on top of an inclined plane having a slope of 3 vertical to 4 horizontal. If the coefficient of friction between the block and the inclined plane is 0.15, determine the force P that may be applied parallel to the inclined plane to keep block from sliding down the plane.

A dockworker adjusts a spring line (rope) which keeps the ship from drifting along side a wharf. If he exerts a pull of 200 N on the rope, which ahs 1 ¼ turns around the mooring bit, what force T can he support? The coefficient of friction between the rope and the cast-steel mooring bit is 0.30.

Determine the distance “x” to which the 90 kg painter can climb without causing the 4m ladder to slip at its lower end A. The top of the 15 kg ladder has a small roller, and the ground coefficient of static friction is 0.25. the lower end of the ladder is 1.5 m away from the wall.

A horizontal force P acts on the top of a 30 kg block having a width of 25 cm, and a height of 50 cm. if the coefficient of friction between the block and the plane is 0.33, what is the value of P for motion to impend?

A 600 N block rests on a 30° plane. If the coefficient of static friction is 0.30 and the coefficient of kinetic friction is 0.20, what is the value of P applied horizontally to prevent the block from sliding down the plane?

A 40 kg block is resting on an inclined plane making an angle of θ from the horizontal. Coefficient of friction is 0.60, find the value of θ when force P = 36.23 is applied to cause the motion upward along the plane.

A 40 kg block is resting on an inclined plane making an angle θ from the horizontal. The block is subjected to a force 87 N parallel to the inclined plane which causes an impending motion down the plane. If the coefficient of motion is 0.60, compute the value of θ.

A rectangular block having a width of 8 cm and height of 20 cm, is resting on a horizontal plane. If the coefficient of friction between he horizontal plane and the block is 0.40, at what point above the horizontal plane should horizontal force P will be applied at which tipping will occur?

Three identical blocks A, B and C are placed on top of each other are place on a horizontal plane with block B on top of A and C on top of B. The coefficient of friction between all surfaces is 0.20. if block C is prevented from moving by a horizontal cable attached to a vertical wall, find the horizontal force in Newton that must be applied to B without causing motion to impend. Each block has a mass of 50 kg.

A car moving downward on an inclined plane which makes an angle of θ from the horizontal. The distance from the front wheel to the rear wheel is 400 cm and its centroid is located at 50 cm from the surface of the plane. If only rear wheels provide breaking, what is the value of θ so that the car will start to slide if the coefficient of friction is 0.6?

A ball is thrown vertically upward with an initial velocity of 3 m/sec from a window of a tall building. The ball strikes at the sidewalk at ground level 4 sec later. Determine the velocity with which the ball hits the ground.

A train starts from rest at station P and stops from station Q which is 10 km from station P. the maximum possible acceleration of the train is 15 km/hour/min. if the maximum allowable speed is 60 kph, what is the least time the train go from P to Q?

A car starting from rest picks up at a uniform rate and passes three electric post in succession. The posts are spaced 360 m apart along a straight road. The car takes 10 sec to travel from first post to sec post and takes 6 sec to go from the second to the third post. Determine the distance from the starting point to the first post.

stone is dropped from the deck of Mactan Bridge. The sound of the splash reaches the deck 3 seconds later. If sound travels 342 m/s in still air, how high is the deck of Mactan Bridge above the water?

At a uniform rate of 4 drops per second, water is dripping from a faucet. Assuming the acceleration of each drop to be 9.81 m/sec2 and no air resistance, find the distance between two successive drops in mm if the upper drop has been in motion for 3/8 seconds.

A racing car during the Marlboro Championship starts from rest and has a constant acceleration of 4 m/sec2. What is its average velocity during the first 5 seconds of motion?

A car accelerates for 6 sec from an initial velocity of 10 m/s. the acceleration is increasing uniformly from zero to 8 m/s^2 in 6 sec. during the next 2 seconds, the car decelerates at a constant rate of m/s^2. Compute the total distance the car has traveled from the start after 8 sec.