I. [ 10 Points] A plant can manufacture 50 golf clubs per day at a total daily cost of $5159and 60 golf clubs per day for a total cost of $5859. Please show all work and calculations. (a) Assuming that daily cost and production are linearly related, find the total daily cost, C, of producing x golf clubs. (b) Graph the total daily cost for 0 5 x 5 200. (c) Interpret the slope and y intercept of the cost equation. 2. [15 Points] A farmer buys a new tractor for S 155.000 and assumes that it will have a trade-in value of $83,000 after 10 years. The farmer uses a constant rate of depreciation to determine the annual value of the tractor. Please show all work and calculations. (a) Find a linear model for the depreciated value V of the tractor t years after it was purchased. (b) What is the depreciated value of the tractor after 6 years? (c) When will the depreciated value fall below $60,000? (d) Graph V for 0 x 5 20. 3. [10 Points] Find the equilibrium point for the pair of demand and supply functions. Here q represents the number of units produced, in thousands, and x is the price, in dollars. Demand: q = 12.000 – 60x Supply: q = 200 + 60x Please show all work and calculations.
4. [20 Points] We found that the marketing research department for the company that manufactures and sells memory chips for microcomputers established the following price-demand functions p(x) = 90 — 3x 1Sx518 where p(x) is the wholesale price in dollars at which x million chips can be sold.
(a) Find and plot the revenue function. R(x).
Please show all work and calculations.
(b) Find the output that will produce the maximum revenue. (c) What is the wholesale price per chip that produces the maximum revenue? 5. [15 Points] The table shows the increase in average monthly price for cable television in the United States since the year 2012.. Pleat* show all work and caicuiations. (a) Using Excel, find a linear regression model for the average monthly price, where x is the number of years since 2012. Please show all work and screen shot excel (b) Interpret the slope of the model. (c) Use the model to predict the average monthly price in 2023.