I would some assistance in solving the following questions

2. If x thousand dollars is spent on labour and y thousand dollars is spent on equipment, the output of a certain factory will be Q(x, y) = 60x1/3y2/3 units. The factory has $120,000 that is available to be allocated to labour and equipment. (i) How much money should be allocated between labour and equipment to generate the largest possible output? (ii) Estimate the change in the maximum output of the factory that will result if the money available for labour and equipment is increased by $1,000. 3. A manufacturer is planning to sell a new product at a price of $150 per unit and estimates that if x thousand dollars is spent on development and y thousand dollars is spent on promotion, approximately 320X 160.x y + 2 + units of the product will be sold. The cost of manufacturing the product is $50 per unit. The manufacturer has a total of $8,000 to spend on development and promotion. (i) How much money should be allocated between development and promotion to generate the largest profit? Note: Profit = (no. of units) (price/unit - cost/unit) - amt. spent on develp. and promo. (ii) Suppose the manufacturer decides to spend $8,100 instead of $8,000 on development and promotion of the new product. Estimate how this change will affect the maximum possible profit. 4. A consumer has $280 to spend on two commodities, the first of which costs $2 per unit and the second $5 per unit. Suppose that the utility derived by the consumer from x units of the first commodity and y units of the second is given by U(x, y) = 100x0.25y0.75 (i) How many units of each commodity should the consumer buy to maximize utility? (ii) Compute the Lagrange multiplier 1 and interpret in economic terms. (In the context of maximizing utility, 1 is called the marginal utility of money.) 5. A consumer has & dollars to spend on two commodities, the first of which costs a dollars per unit and the second b dollars per unit. Suppose that the utility derived by the consumer from x units of the first commodity and y units of the second commodity is given by the Cobb - Douglas utility function U(x, y) = xay, where 0