1.)

Find the cost function for the marginal cost function. 70 e 0.01x F'(x) = + 200; 3 units cost $1600. <:> F(x) = D (Simplify your answer. Use integers or decimals for any numbers in the expression rounded to the nearest hundredth as needed.) 48x 4x2+ e A company has found that the marginal cost (in thousands of dollars) to produce x central air conditioning units is C'(x) = , where x is the number of units produced. (a) Find the cost function, given that the company incurs a fixed cost of $16,000 even if no units are built. (b) The company will seek a new source of investment income if the cost is more than $24,000 to produce 5 units. Should they seek this new source? E) (a) What substitution should be used to determine the cost function? Use the quantity :1 as the substitution, u = D, so that du = (D) dx. The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the following function. The revenue from 115 gadgets is $3,863. 2 MR(x)=4x(x2 + 26,000) 3 (3) Find the revenue function. (b) What is the revenue from selling 250 gadgets? (6) How many gadgets must be sold for a revenue of at least $30,000? <:> (a) R(x) = D (Simplify your answer. Round to the nearest integer as needed.) 44 The number ofjobs in the mining industry is changing at a rate (in thousands ofiobs per year) approximated by f(x) = m, where x = 0 corresponds to the year 2000. There were 510,000 mining industry jobs in 2000. (3) Find the function giving the number of mining industry jobs in year x. (b) Find the projected number of mining industn/ jobs in the year 2020. (a) Set up the appropriate integral that can be used to nd the number of mining industry jobs. I( dx