Question
In: Advanced Math
Your firm produces two products, Thyristors (T) and Lozenges (L), that compete for the scarce resources...
Your firm produces two products, Thyristors (T) and Lozenges (L), that compete for the scarce resources of your distribution system. For the next planning period, your distribution system has available 6,000 person-hours. Proper distribution of each T requires 3 hours and each L requires 2 hours. The profit contributions per unit are 40 and 30 for T and L, respectively. Product line considerations dictate that at least 1 T must be sold for each 2 L’s.
(a) Draw the feasible region and draw the profit line that passes through the optimum point.
(b) What are the constraints for this problem?
(c) By simple common sense arguments, what is the optimal solution?
Solutions
Colby Messinger answered 7 months agoRelated Solutions
Consider two firms, Firm A and Firm B, who compete as duopolists. Each firm produces an...
Consider two firms, Firm A and Firm B, who compete as
duopolists. Each firm produces an identical product. The total
inverse demand curve for the industry is
P=250-QA+QB.
Firm A has a total cost curve
CAQA=100+QA2.
Firm B has a total cost curve
CBQB=100+2QB.
Suppose for now, only Firm A exists
(QB=0). What is the Monopoly equilibrium
quantity and price? What is Firm A’s profit?
Find the Nash Cournot equilibrium price and output level. What
are the firms’ profits?
Find...
what is change in your view on using scarce resources and how?
what is change in your view on using scarce resources and
how?
Suppose that your firm produces two products in fixed proportions, so that if you decide to...
Suppose that your firm produces two products in fixed
proportions, so that if you decide to produce one more unit of X,
your firm must also produce one more unit of Y. If TC = 100 + 3Q
+½Q2 and the demand curves for X and Y are
QX=100-2PX, and
QY=101-PY find the profit maximizing
outputs.
(a) Find the expressions for MR for good X and good Y. (Hint: solve
each demand curve for P, multiply by Q, take the...
2. Suppose an industry consists of two firms that compete in prices. Each firm produces one...
2. Suppose an industry consists of two firms that compete in
prices. Each firm produces one product. The demand for each product
is as follows:
q1 = 25 − 5p1 + 2p2
q2 = 25 − 5p2 + 2p1
The cost functions are C(qi) = 2 + qi for i = 1, 2.
The Nash equilibrium price is 3.75
(e) What is the percentage markup of price over marginal cost
here (this is called the Lerner index)? Do the firms...
Henna Co. produces and sells two products, T and O. It manufactures these products in separate...
Henna Co. produces and sells two products, T and O. It
manufactures these products in separate factories and markets them
through different channels. They have no shared costs. This year,
the company sold 43,000 units of each product. Sales and costs for
each product follow.
Product T
Product O
Sales
$
761,100
$
761,100
Variable costs
608,880
76,110
Contribution margin
152,220
684,990
Fixed costs
33,220
565,990
Income before taxes
119,000
119,000
Income taxes (30% rate)
35,700
35,700
Net income
$...
Letter Co. produces and sells two products, T and O. It manufactures these products in separate...
Letter Co. produces and sells two products, T and O. It
manufactures these products in separate factories and markets them
through different channels. They have no shared costs. This year,
the company sold 48,000 units of each product. Sales and costs for
each product follow.
Product T
Product O
Sales
$
825,600
$
825,600
Variable costs
577,920
165,120
Contribution margin
247,680
660,480
Fixed costs
113,680
526,480
Profit before taxes
134,000
134,000
Income taxes (32% rate)
42,880
42,880
Net
profit
$...
Letter Co. produces and sells two products, T and O. It manufactures these products in separate...
Letter Co. produces and sells two products, T and O. It
manufactures these products in separate factories and markets them
through different channels. They have no shared costs. This year,
the company sold 53,000 units of each product. Sales and costs for
each product follow.
Product T
Product O
Sales
$
863,900
$
863,900
Variable costs
604,730
86,390
Contribution margin
259,170
777,510
Fixed costs
116,170
634,510
Profit before taxes
143,000
143,000
Income taxes (40% rate)
57,200
57,200
Net
profit
$...
Letter Co. produces and sells two products, T and O. It manufactures these products in separate...
Letter Co. produces and sells two products, T and O. It
manufactures these products in separate factories and markets them
through different channels. They have no shared costs. This year,
the company sold 53,000 units of each product. Sales and costs for
each product follow.
Product T
Product O
Sales
$
863,900
$
863,900
Variable costs
604,730
86,390
Contribution margin
259,170
777,510
Fixed costs
116,170
634,510
Profit before taxes
143,000
143,000
Income taxes (40% rate)
57,200
57,200
Net
profit
$...
Letter Co. produces and sells two products, T and O. It manufactures these products in separate...
Letter Co. produces and sells two products, T and O. It
manufactures these products in separate factories and markets them
through different channels. They have no shared costs. This year,
the company sold 48,000 units of each product. Sales and costs for
each product follow.
Product T
Product O
Sales
$
825,600
$
825,600
Variable costs
577,920
165,120
Contribution margin
247,680
660,480
Fixed costs
113,680
526,480
Profit before taxes
134,000
134,000
Income taxes (32% rate)
42,880
42,880
Net
profit
$...
Henna Co. produces and sells two products, T and O. It manufactures these products in separate...
Henna Co. produces and sells two products, T and O. It
manufactures these products in separate factories and markets them
through different channels. They have no shared costs. This year,
the company sold 58,000 units of each product. Sales and costs for
each product follow.
Product T
Product O
Sales
$
974,400
$
974,400
Variable costs
779,520
194,880
Contribution margin
194,880
779,520
Fixed costs
46,880
631,520
Income before taxes
148,000
148,000
Income taxes (32% rate)
47,360
47,360
Net income
$...
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