Math Functions

MAC1105 Project # 2

The cost of refurbishing a farm property. Optimization parameters.

*********** THE LAST TWO DIGITS OF MY ID IS 15************

The situation is to set for the purchase of a rectangular farm with a circular pond inside.

The farm needs fencing and planting grass for further minor poultry intensive production.

The cost of the grass is $2.25 per square foot delivered and planted and the cost of the fence is $625 per 100 ft delivered and installed in site.

The dimensions of the farms are Length(L); Width (W); and Diameter of the pond (D) all in feet and proportional to your personal last two digits numbers (ID) of your MDC ID. (if your last two digits are 00, please consider them as the first two instead)

X (thousands of sold units); Revenue (R(X) thousand dollars); Total Cost (C(X) Thousand dollars);

Profit P(X) = R(X) – C(X); the market equilibrium is reached when unit price

p= 200-0.42X ($/sold item)

Given that L= 32.50*(ID); W = 27.50*(ID); D = 3.4*(ID); X = 7.2 *(ID) thousand sold units; R(X)=135.2X-0.038X^2; C(X) = 4.53 X + cost of investment

TASK: In word document (including writing and graphical work) submit via MDC email by February 22, 2021, 11:59 PM; the explanation and the procedure to determine the total cost of the investment in your farm; The level of sales that maximizes profit and the unit price that maximizes revenue. Use the graphs of the profit and revenue functions to show the maximum values.

Directions:

1) Your last two digits number from your ID

2) Compute L, W, D, X

3) Sketch in graph paper, using scale and instruments, the farm with its components

4) Compute the grass area. Use proper units. Show work.

5) Compute the Total length to fence, include internal necessary fence. Use proper units. Show work.

6) Compute total cost of grassing and fencing the farm.

7) Construct the Revenue function, the total cost function and the Profit function

8) Determine the sales to maximize Profit. Use also, in addition, graphical construction to show result

9) Considering the relation between unit price (p) and sold items (X), determine the unit price to maximize Revenue. Use also, in addition, graphical construction to show result.

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