Final answer:
i) The minimum number of units that should be produced and sold to ensure no loss is 400. ii) The new breakeven point is 500 units. To guarantee no loss, the price per unit should be ₹39.
Step-by-step explanation:
i) To ensure no loss, the revenue generated should be equal to or greater than the cost. In this case, the revenue is given by the selling price multiplied by the number of units sold. Let's assume the minimum number of units to be produced and sold is 'y'. So, the revenue equation becomes: R(y) = 30y. To find the minimum number of units, we need to solve the equation R(y) = C(y), where C(y) is the cost equation. Substituting the given cost equation, we get: 30y = 17.5y+7000. Solving this equation, we find y = 400. Therefore, the minimum number of units that should be produced and sold to ensure no loss is 400.
ii) If the selling price is reduced by ₹3/unit, the new selling price becomes 30-3 = ₹27/unit. To find the new breakeven point (BEP), we need to solve the equation R(y) = C(y), where R(y) is the revenue equation and C(y) is the cost equation. Substituting the new selling price and cost equation, we get: 27y = 17.5y+7000. Solving this equation, we find y = 500. Therefore, the new breakeven point is 500 units.
To guarantee no loss, the selling price should be such that the revenue is equal to or greater than the cost. Using the new breakeven point (500 units) and the cost equation, we can solve for the selling price. Substituting the values, we get: 500p = 17.5(500)+7000. Solving this equation, we find p = ₹39. Therefore, the price per unit that should be charged to guarantee no loss is ₹39.