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i. The Students Union of a University plans to have an end-of-year party for all its members. The party is scheduled to take place at a major hotel that can accommodate up to 500 persons. The hotel was to charge N800 per person. At this gate fee, the hotel expects to sell 400 tickets. Market research postulates that for every N40 increase or reduction in the ticket price, the demand will fall or increase by 16 tickets.
Required:
If the variable cost per student for the dinner is N210, determine the Marginal Revenue (MR) function.
(6 marks)
ii. JANG PLC produces and sells two products G and H. G and H respectively make contributions of N10 and N15. The company wishes to maximize its profit. 4,150 units and 3,175 units of G and H, respectively, are to be sold. Direct labor hours per unit are 2.5 hours and 1.5 hours for G and H, while machine hours per unit are 45 minutes and 3 hours for G and H, respectively. Total direct labor hours available and total machine hours available are, respectively, 18,000 hours and 10,000 hours.
Required:
Derive the following constraints: the direct labor, machine time, sales demand for G, sales demand for H, and non-negativity constraints. (4marks)
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A manufacturer determines that the firm’s Marginal Cost (MC) and Marginal Revenue (MR) functions are:
MC=C′(x) = 100 − 0.1x
MR = R′(x)=100 + 0.1x
You are required to find the:
a. Change in revenue that results when the sales level increases from 20 to 30 units. (5 Marks)
b. Revenue resulting from the sale of 30 units. (5 Marks)
c. Cost of producing 30 units if the fixed cost (at x=0x = 0) is N400. (5 Marks)
d. Total profit when 30 units of the product are sold. (5 Marks)
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Kyerewaa Ventures is a manufacturing company in the business of producing beverage cans for clients in the brewery industry. The weekly total cost to produce x cans is given by:
The demand function for the cans is given by:
The company has set a production limit to 10,000 cans and it sells all the cans that are produced.
Required:
i) Derive an expression for marginal cost, marginal revenue, and marginal profit. (4 marks)
ii) Determine the cost, revenue, and profit when the 2,501st can is produced and sold. (3 marks)
iii) Determine the cost, revenue, and profit when the 7,501st can is produced and sold. (3 marks)
iv) Advise the company whether to produce the 2,501st can or the 7,501st can. (2 marks)
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a) The marginal revenue function of a manufacturing company is given by:
The marginal cost function is given by:
Let x be the number of items either produced or sold.
Required:
i) Calculate the revenue generated when 50 items are sold. (2 marks)
ii) Calculate the number of items that will yield maximum revenue. (4 marks)
iii) Calculate the total revenue if 100 items are produced. (4 marks)
iv) Calculate the total profit for the 100 items. (4 marks)
v) If a tax of 20% is imposed on each item produced, find the cost of 100 items. (6 marks)
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A TV manufacturer finds that he can sell xx units per week at a price p=250−0.5xp = 250 – 0.5x each. His cost of production of xx TV sets per week is given by C=240+2xC = 240 + 2x.
Required:
(i) Determine how many sets per week he should produce to maximize his profit. (5 Marks)
(ii) Determine the maximum profit. (2 Marks)
Find Related Questions by Tags, levels, etc.
Find Related Questions by Tags, levels, etc.
i. The Students Union of a University plans to have an end-of-year party for all its members. The party is scheduled to take place at a major hotel that can accommodate up to 500 persons. The hotel was to charge N800 per person. At this gate fee, the hotel expects to sell 400 tickets. Market research postulates that for every N40 increase or reduction in the ticket price, the demand will fall or increase by 16 tickets.
Required:
If the variable cost per student for the dinner is N210, determine the Marginal Revenue (MR) function.
(6 marks)
ii. JANG PLC produces and sells two products G and H. G and H respectively make contributions of N10 and N15. The company wishes to maximize its profit. 4,150 units and 3,175 units of G and H, respectively, are to be sold. Direct labor hours per unit are 2.5 hours and 1.5 hours for G and H, while machine hours per unit are 45 minutes and 3 hours for G and H, respectively. Total direct labor hours available and total machine hours available are, respectively, 18,000 hours and 10,000 hours.
Required:
Derive the following constraints: the direct labor, machine time, sales demand for G, sales demand for H, and non-negativity constraints. (4marks)
Find Related Questions by Tags, levels, etc.
A manufacturer determines that the firm’s Marginal Cost (MC) and Marginal Revenue (MR) functions are:
MC=C′(x) = 100 − 0.1x
MR = R′(x)=100 + 0.1x
You are required to find the:
a. Change in revenue that results when the sales level increases from 20 to 30 units. (5 Marks)
b. Revenue resulting from the sale of 30 units. (5 Marks)
c. Cost of producing 30 units if the fixed cost (at x=0x = 0) is N400. (5 Marks)
d. Total profit when 30 units of the product are sold. (5 Marks)
Find Related Questions by Tags, levels, etc.
Kyerewaa Ventures is a manufacturing company in the business of producing beverage cans for clients in the brewery industry. The weekly total cost to produce x cans is given by:
The demand function for the cans is given by:
The company has set a production limit to 10,000 cans and it sells all the cans that are produced.
Required:
i) Derive an expression for marginal cost, marginal revenue, and marginal profit. (4 marks)
ii) Determine the cost, revenue, and profit when the 2,501st can is produced and sold. (3 marks)
iii) Determine the cost, revenue, and profit when the 7,501st can is produced and sold. (3 marks)
iv) Advise the company whether to produce the 2,501st can or the 7,501st can. (2 marks)
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a) The marginal revenue function of a manufacturing company is given by:
The marginal cost function is given by:
Let x be the number of items either produced or sold.
Required:
i) Calculate the revenue generated when 50 items are sold. (2 marks)
ii) Calculate the number of items that will yield maximum revenue. (4 marks)
iii) Calculate the total revenue if 100 items are produced. (4 marks)
iv) Calculate the total profit for the 100 items. (4 marks)
v) If a tax of 20% is imposed on each item produced, find the cost of 100 items. (6 marks)
Find Related Questions by Tags, levels, etc.
A TV manufacturer finds that he can sell xx units per week at a price p=250−0.5xp = 250 – 0.5x each. His cost of production of xx TV sets per week is given by C=240+2xC = 240 + 2x.
Required:
(i) Determine how many sets per week he should produce to maximize his profit. (5 Marks)
(ii) Determine the maximum profit. (2 Marks)
Find Related Questions by Tags, levels, etc.
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what is the marginal revenue when