# Algebra - Equations and Matrices

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Exercise 5.5

25. Supply and Demand The supply function for a product is given by p=q²+2q+122 and the demand function for this product is p=650-30q, where p is the price in dollars and q is the number of hundreds of units. Find the price that gives market equilibrium and the equilibrium quantity.

29. Break-Even The weekly total cost function for a piece of equipment is C(x) =2000x+ 18,000+60x² dollars, and the weekly revenue is R(x) =4620x-12x²-x³, where x is the number of thousands of units. The x-values that are the solution to the system

y=2000x+18,000+60x²

y=4620x-12x²-x³

are the quantities that give break-even. Find these quantities.

31. Break-Evan The monthly total cost function for a product is C(x) =400x+0.1x²+17,901 dollars, and the monthly revenue is R(x) =1000x-0.01x², where x is the number of units. Find the numbers of units that's give break-even for the product. (Hint: Use graphical methods to find one solution less than 100 units and one greater than 5000 units.)

33.Construction a Box A rectangular piece of cardboard with area 180 square inches is made in to an open box by cutting squares 2 inches on a side from each corner and turning up the sides. If the box is to have a volume of 176 cubic inches, what is the dimension of the original piece of cardboard?

2 2

2 2

2 2

2 2

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#### Solution Preview

Exercise 5.5

25. Supply and Demand The supply function for a product is given by p=q²+2q+122 and the demand function for this product is p=650-30q, where p is the price in dollars and q is the number of hundreds of units. Find the price that gives market equilibrium and the equilibrium quantity.

For market equilibrium, supply = demand

q^2 + 2q + 122 = 650 - 30q

q^2 + 32q - 528 = 0

On solving, we get q = {-44, 12}

The equilibrium quantity is 12 units

The equilibrium price is 650 - 30(12) = $290.

29. Break-Even The weekly total cost function for a piece of equipment is C(x) =2000x+ 18,000+60x² dollars, and the weekly revenue is R(x) =4620x-12x²-x³, where x is the number of thousands of units. The x-values that are the solution to the system

...

#### Solution Summary

Equations for matrices are used to examine the supply function using algebra. A complete, neat and step-by-step solutions are provided in the attached file.