The profit function for a computer company is given by P(c) = - + 30x - 22 where a is the number of units produced (in thousands) and the profit is in thousand of dollars. a) Determine how many (thousands of) units must be produced to yield maximum profit. Determine the maximum profit. (thousands of) units = maximum profit = thousand dollars b) Determine how many units should be produced for a profit of at least 40 thousand. more than (thousands of) units less than (thousands of) unitsThe cost of producing m units of a product is given by Om) : 800 + 1203; 12UIn(m), :e 2 1' Find the minimum average cost Minimum Average Cost = [:J The revenue from selling q items is R(q) = 450q - q2, and the total cost is C(q) = 100 + 5q. Write a function that gives the total profit earned, and find the quantity which maximizes the profit. Profit TT (q) = Quantity maximizing profit q =A manufacture has been selling 1450 television sets a week at $390 each A market survey indicates that for each $30 rebate offered to a buyer, the number of sets sold will increase by 300 per week. a) Find the function representing the demand p(x} where 1' is the number of the television sets sold per week and p(:v} is the corresponding price 13(1) = Cl b) How large rebate should the company offerto a buyer, in orderto maximize its revenue?[ ldollais c) lfthe weekly cost function is 94250 + 13031:, howI should it set the size of the rebate to maximize its profit?| J dollars The price (in dollars) p and the quantity demanded q are related by the equation: p3 + 2q = 1100. If R is revenue, d , dh can be expressed by the following equation: OR = Asp where A is a function of just q. A Find dR dt when q = 15 and- AP = 4. dt d.R. it dp Hint: Remember that R = pq, so an FPdi da + 9 d'(Once you have their money. nevergive it back.) An apartment complex on Ferenginar with 250 units currently ha5182 occupants. The current rent for a unit is 910 slips of Goid Pressed Latinum. The owner of the complex knows from experience that he loses one occupant ever}.r time he raises the rent by 2.5 Slips of Latinum' Since "profit is its own reward". the owner wants to maximize his prot so he asks for our help, even though he knows that "free advice is seldom cheap". What should be our recommendation for the optimal rent? I lslips of Gold-Pressed Latinum A baseball team plays in a stadium that holds 50000 spectators With the ticket price at $8 the average attendance has been 22000. When the price dropped to $1 the average attendance rose to 25000. a) Find the demand function 33(2). where a: is the number of the spectators (Assume thatp{a:) is linear.) 10(16) = [j b) How should ticket prices be set to maximize revenue? The revenue is maximized by charging 55' 7.6? lper ticket