Alpha Electronics Produces Sophisticated Business Computers

question 61

Essay

Alpha Electronics produces sophisticated business computers. Its subsidiary, HRD Drives, produces hard disks which Alpha uses in each computer. HRD operates in a competitive market; each disk sells for $120.00 on the open market. Management has determined that the demand curve for quantity sold per month of the computers is:
Q_c = 8,000 - .4P_c
while Alpha's marginal cost for the computers, excluding the cost of the disks is:
MC_c = 5Q_c
In addition, management has determined that the total cost function for the disks is:
TC_d = 18Q_d + .0075Q_d²
a. At what final product price and rate of output will the firm maximize profit?
b. How much of the transfer product should be produced?
c. Should the final product division obtain all of its disks for the computers from HRD Drives? Why or why not?

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Definitions:

Real Number

A value that represents a quantity along a continuous line, including both rational and irrational numbers.

Arithmetic Operators

Operators in programming that perform mathematical calculations such as addition, subtraction, multiplication, division, and modulus.

Operand

An object that is manipulated by an operator in a mathematical operation or expression.

Literal Value

A fixed value explicitly presented in source code, such as numerical constants, character constants, or string literals.