Solve the problem. suppose an economy consists of three sectors: energy (e), manufacturing (m), and agriculture (a). sector e sells 70% of its output to m and 30% to a. sector m sells 30% of its output to e, 50% to a, and retains the rest. sector a sells 15% of its output to e, 30% to m, and retains the rest. denote the prices (dollar values) of the total annual outputs of the energy, manufacturing, and agriculture sectors by pe, pm, and pa, respectively. if possible, find equilibrium prices that make each sector's income match its expenditures. find the general solution as a vector, with pa free.

You are thinking of making your mansion more energy efficient by replacing some of the light bulbs with compact fluorescent bulbs, and insulating part or all of your exterior walls. each compact fluorescent light bulb costs $4 and saves you an average of $2 per year in energy costs, and each square foot of wall insulation costs $1 and saves you an average of $0.20 per year in energy costs.† your mansion has 150 light fittings and 3000 sq ft of uninsulated exterior wall. to impress your friends, you would like to spend as much as possible, but save no more than $750 per year in energy costs (you are proud of your large utility bills). how many compact fluorescent light bulbs and how many square feet of insulation should you purchase? how much will you save in energy costs per year? (if an answer does not exist, enter dne.)

Randall's, inc. has 20,000 shares of stock outstanding with a par value of $1.00 per share. the market value is $12 per share. the balance sheet shows $42,000 in the capital in excess of par account, $20,000 in the common stock account, and $50,500 in the retained earnings account. the firm just announced a 5 percent (small) stock dividend. what will the balance in the retained earnings account be after the dividend?

Oerstman, inc. uses a standard costing system and develops its overhead rates from the current annual budget.the budget is based on an expected annual output of 120,000 units requiring 480,000 direct labor hours.(practical capacity is 500,000 hours)annual budgeted overhead costs total $772,800, of which $556,800 is fixed overhead.a total of 119,300 units, using 478,000 direct labor hours, were produced during the year.actual variable overhead costs for the year were $260,400 and actual fixed overhead costs were $555,450.required: 1. compute the fixed overhead spending variance and indicate if favorable or unfavorable.2. compute the fixed overhead volume variance and indicate if favorable or unfavorable.