(a) output (Q): (1) € integral for the following marginal MR = f(Q) = Q³-50² + √Q MR = f(Q) = (Q+1)² enue functions with respect to Hint: You use the result f¹dQ = log (Q-1) + C
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- As a producer and seller of some commodity, you have learned that, if you produce and sell x itmes in a particular month, the following functions can be used to find the cost and revenue: Revenue: R(x)=150x-x^2 and Cost: C(x)=3000+20x. (a) Write a simplified formula for your profit in a particular month, P(x)=R(x)- C(x) (b) Find the "break-even" point(s) (c) How many items should you produce and sell in a month in order to achieve a maximum profit? (d) What is the maximum possible monthly profit? This is the problem and I cannot solve the c and d, could you please help me?1. For each of the cost functions given below, do the following things: C(T) = = 10 + 2T. C(T) = T0.8 (a) Draw the graph for C(T), with T on the horizontal axis. Explicitly the values for the intercepts. (b) Derive AC and MC respectively, and draw their curves. (c) Determine whether the cost function exhibits IRTS or DRTS or CRTS.A firm has the following production function: Q = 9L2/3K1/3 Where Q is output, L is labor and K is Capital. Where Q is output, L is labor and K is Capital. (a) What sort of returns to scale characterize this production function? (b) Derive the marginal product of labor and capital. (c) What do we mean when we say the production function is linearly homogenous?
- A factory makes bicycle tires. The cost, C, in dollars and revenuue in dollars, R, are both functions of the number of tires, n.a) Describe what is meant by C'(4) = 8b) Generate a mathematical equation, using function notation, to model the following statements: for (b) + (c) "The marginal revune for 15 tires sold decreases by $1."c) "The revenue at 3 tires equals the change in cost at 5 tires"(b) A firm has an average cost function 125 q? 4. 16 A(q) %3D - where q is the firm's output. (i) Determine the level of output for average costs are minimum. (ii) Hence determine the range of values for which average costs are decreasing. (iii) What part of the decreasing range is practically feasible?(i) Find the rate of change of the function f(x) =x + 2/ 1 − 8x with respect to x when x = 1.(ii) The number of units Q of a particular commodity that will be produced with Kthousand dollars of capital expenditure is modeled by Q(K) = 500 K2/3Suppose that capital expenditure varies with time in such a way that t months from nowthere will be K(t) thousand dollars of capital expenditure, whereK(t) =2t4 + 3t + 149 / t + 2 (a) What will be the capital expenditure 3 months from now? How many units will be producedat this time?(b) At what rate will production be changing with respect to time 5 months from now?Will production be increasing or decreasing at this time?
- It costs a baker a fixed cost of $420 and variable cost of $2.10 per cupcake. A cupcake issold for $4.90 each.(i) Make a table showing the total cost and the revenue obtained from producing 20,40,60,80 and 100 cupcakes.(ii) Write algebraic expressions representing the cost C and the revenue R as functions of the number of cupcakes X produced and number of cupcakes X sold respectively.(iii) Graph both functions on the same coordinate axes and from your graph determine the cordinate at which cost equals revenue.F Given Cost and Revenue functions C(q)=q³-8q² +59q + 5000 and R(q) = -3 -39² +2600q, what cost is incurred when marginal profit is $0? The costs are $ (Round to nearest cent.)The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given by the following function. )= 4x (x² +27,000) 4x R'(x) = 2 (a) Find the total revenue function if the revenue from 130 devices is $21,660. (b) How many devices must be sold for a revenue of at least $38,000? BECED (a) The total revenue function is R(x)=, given that the revenue from 130 devices is $21,660. (Round to the nearest integer as needed.) (b) devices must be sold to generate a revenue of at least $38,000. (Type a whole number.)
- Q4 The output of a production process, Q, is given by the function KL Q = K+ 2L where K and L denote capital and labor. (a) Calculate the output when the capital and labor are 40 and 30 units, respectively. (b) Find the level of labor needed to produce 4 units of output when 10 units of capital are used. (c) Transpose this formula to express K in terms of Q and L. Q5 3 The equations defining a simple model of the economy are: C = 0.75Y + 18 I = 22 where C, Y and I denote consumption, national income and planned investment, respectively. Use this model to complete the following table of values and hence draw an accurate graph of C + I plotted against Y on the interval 0 < Y< 200. 100 200 C + I By drawing a second line on the diagram, calculate the equilibrium level of national income. Use your graph to explain what happens to the equilibrium level of national income when the marginal propensity to consume decreases with autonomous consumption fixed.A firm uses a single input to produce a commodity according to itsshort-run production function f(x) = 4√x, where x is the number of units ofinput. The commodity sells for $100 per unit. The input cost $50 per unit.(a) Write down a function that states the firm’s profit as a function ofthe amount of input.(b) What is the profit maximizing amount of input and output?(c) Suppose the firm is taxed $20 per unit of its output and the priceof its input is subsidized by $10, explain in detail how this will affect the newinput and output levels?(b) A firm has an average cost function A(q) = 125 q + q 2 16 − 4. where q is the firm′ s output. (i) Determine the level of output for average costs are minimum. (ii) Hence determine the range of values for which average costs are decreasing. (iii) What part of the decreasing range is practically feasible? (iv) Write an equation for the total cost function. (v) Hence calculate the level of output for which total costs are minimum. Can I get the answer for (iv) and (v) please