Question

Each unit of a product can be made on either machine A or machine B. The nature of the machines makes their cost functions differ.

Machine A: 30+ (x^2) / 6

Machine B: C (y) =180 + (y ^3) / 9

Total cost is given by C(x,y)= C(x)+ C(y). How many units should be made on each machine in order to minimize total costs if x+y=14,520 units are required?

The minimum total cost is achieved when ----------? units are produced on machine A and --------------? units are produced on machine B. (Simplify your answer.)

Answer #1

Each unit of a product can be made on either machine A or
machine B. The nature of the machines makes their cost functions
differ.
Machine A: C(x)= 60+x^2/6
Machine B: C(y)= 240+y^3/9
Total cost is given by
C(x,y)equals=Upper C left parenthesis x right
parenthesisC(x)plus+Upper C left parenthesis y right
parenthesisC(y).
How many units should be made on each machine in order to
minimize total costs if
xplus+yequals=22 comma 65022,650
units are required?
The minimum total cost is achieved when...

Each unit of a product can be made on either machine A or
machine B. The nature of the machines makes their cost functions
differ.Total cost is given by C(x,y)equalsUpper C left parenthesis
x right parenthesisplusUpper C left parenthesis y right
parenthesis. How many units should be made on each machine in order
to minimize total costs if x+y=19,740 units are required?
c(x)=50+(x^2/6) c(y)=160+(y^3)/9.

A company manufactures x units of Product A
and y units of Product B, on two machines, I and
II. It has been determined that the company will realize a profit
of $4/unit of Product A and a profit of $3/unit of Product
B. To manufacture a unit of Product A requires 6
min on Machine I and 5 min on Machine II. To manufacture a unit of
Product B requires 9 min on Machine I and 4 min on...

A company can sell all the units it can produce of either
Product A or Product B but not both. Product A has a unit
contribution margin of $18 and takes two machine hours to make and
Product B has a unit contribution margin of $30.0 and takes three
machine hours to make. If there are 5000 machine hours available to
manufacture a product, income will be
$5000 less if Product A is made.
$5000 less if Product B is...

A company can sell all the units it can produce of either
Product A or Product B but not both. Product A has a unit
contribution margin of $8 and takes two machine hours to make and
Product B has a unit contribution margin of $22.5 and takes three
machine hours to make. If there are 5000 machine hours available to
manufacture a product, income will be $17500 less if Product B is
made. $17500 more if Product A is...

A company manufactures x units of Product A
and y units of Product B, on two machines, I and
II. It has been determined that the company will realize a profit
of $5/unit of Product A and a profit of $2/unit of Product
B. To manufacture a unit of Product A requires 6
min on Machine I and 5 min on Machine II. To manufacture a unit of
Product B requires 9 min on Machine I and 4 min on...

A cell phone battery can be produced by machine A, machine B, or
machine C. Twenty percent of the time the battery will be produced
by machine A, 45% by machine B, and 35% by machine C. A quality
control analyst inspects the batteries after production and finds
that machine A makes defective batteries 10% of the time, where
machines B and C each makes defective batteries 8% of the time.
One cell phone battery is randomly selected from the...

A manager must decide which type of machine to buy, A,
B, or C. Machine costs (per individual machine) are as
follows:
Machine Cost
A $40,000
B $30,000
C $80,000
Product forecasts and processing times on the machines
are as follows:
Product Annual Processing Time Per
Demand
A B C
1 18,000 4 2 1
2 20,000 1 5 3
3 20,000 5 6 6
4 16,000 4 6 3
a)Assume that only purchasing costs are being considered.
Compute the...

If the total cost function for a product is C(x) = 9(x + 3)^3
dollars, where x represents the number of hundreds of units
produced, producing how many units will minimize average cost?
a) x= ?
b) Find the minimum average cost per hundred units.

In Zhuang LTD , data concerning two products are Contribution
margin per unit—Product A $10, Product B $12; machine hours
required for one unit—Product A 2, Product B 3.
a) Calculate the contribution margin per unit of the limited
resource for each product:
Product A: $ Answer per hour
Product B: $ Answer per hour
b) If Zhuang LTD has a limited number of machine hours and can sell
all the units produced of either product, which product should it...

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