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3 years ago

Given the Production Function Q = 72X + 15X2 - X3, where Q =Output and X=Input

Business

1 answer:

Gnom [1K]3 years ago

4 0

Answer:

A. 120

B. 126

C. x=12

D. x=5

Explanation:

A. Calculation to determine the Marginal Product (MP) when X = 8

Production function=Q=72x+15x^2-x^3

Let x be 8

Marginal Product (MP)=dQ/dx

Marginal Product (MP)=72x+15x^2-x^3

Marginal Product (MP)=72+30x-3x^2

Now let plug in X = 8

Marginal Product (MP)=72+30(8)-3(8)^2

Marginal Product (MP)=72+240-192

Marginal Product (MP)=120

Therefore the Marginal Product (MP) when X = 8 will be 120

B. Calculation to determine the Average Product (AP) when X = 6

Average Product (AP)=Q/X

Average Product (AP)=72+15x-x^2

Let plug in x=6

Average Product (AP)=72+15(6)-(6)^2

Average Product (AP)=72+90-36

Average Product (AP)=126

Therefore the Average Product (AP) when X = 6 is 126

C. Calculation to determine at what value of X will Q be at its maximum

Maximizing Q=dQ/dx=0

Maximizing Q=72+30x-3x^2=0

Maximizing Q=3x^2-30x-72=0

Maximizing Q=x^2-10x-24=0

Maximizing Q=x^2-12x+2x-24=0

Maximizing Q=x(x-12)+2(x-12)=0

Hence:

x=12 or (x=-2)

Therefore at what value of X will Q be at its maximum will be at x=12

D. Calculation to determine At what value of X will Diminishing Returns set in

Diminishing returns=dMP/dx=d²Q/dx²

Diminishing returns=30-6x<0

Hence:

x=30/6<0

x=5<0

Therefore at what value of X will Diminishing Returns set in will be at x= 5 or when MP is at a MAXIMUM VALUE.

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Answer:

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1 year ago

Identify the phase (Phillips, stagflation, or recovery) the economy is in, and suggest what change in aggregate demand or aggreg

Annette [7]

Answer:

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b. "The nation's inflation rate rose to a record high last month, the government reported yesterday. The consumer price index jumped 0.3% in January. Coupled with the announcement earlier this month that unemployment had risen by 0.5 percentage points, the reports suggested that the first month of President Nixon's second term had gotten off to a rocky start."

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4 years ago

Ralph Lauren sells suits and ties. Suits sell for $1000 each, and cost $300 in variable expenses to make each. Ties sell for $10

lina2011 [118]

Answer:

Weighted average contribution margin ratio= $632.5

Explanation:

Giving the following information:

Suits:

Selling price= $1,000

Unitary variable cost= $300

Sales participation= 90%

Ties:

Selling price= $100

Unitary variable cost= $75

Sales participation= 10%

To calculate the weighted contribution ratio, we need to use the following formula:

Weighted average contribution margin ratio= weighted average selling price - weighted average unitary varialble cost

weighted average selling price= (1,000*0.9) + (100*0.1)= 910

weighted average unitary varialble cost= (300*0.9) + (75*0.1)= 277.5

Weighted average contribution margin ratio= 910 - 277.5= $632.5

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3 years ago

Suppose that Larimer Company sells a product for $24. Unit costs are as follows:

yanalaym [24]

Answer:

Variable cost per unit=$10.08

Contribution per unit=$13.92

Contribution margin ratio=58%

Variable cost ratio= 42%

c) Break-even units=3,000 units

Explanation:

Variable cost per unit

= 4.98 + 2.10 + 1.00 + 2.00 = $10.08

Variable cost per unit=$10.08

Contribution per unit = Selling price per unit - Variable cost per unit

= 24 - 10.08 =13.92

Contribution per unit=$13.92

Contribution margin ratio= contribution/selling price= 13.92/24 × 100=58%

Contribution margin ratio=58%

Variable cost ratio = variable cost/selling price= 10.08 /24× 100 = 42%

Variable cost ratio=42%

Break-even units = Total general fixed cost/contribution per unit

= (26,500 + 15,260)/ 13.92 = 3000 units

Break-even units=3,000 units

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3 years ago