Modern Home Sdn$.$ Bhd$.$ manufactures four types of multi$-$purpose storage cabinets: Modern, Antique, Trendy and Smart. The selling price and the marginal cost of each product are as follows

Modern Antique Trendy Smart

RM RM RM RM

Selling Price $220340440280$

Marginal cost $84104144124$

The company$$s fixed costs are RM$150,000$ per annum. There is a shortage of a raw material called Glossy Melamine which is used in all four products. Modern uses $20$ ml of Glossy Melamine, Antique $20$ ml$,$ Trendy $28$ ml and Smart $30$ ml$.$ Only $300,000$ ml of Glossy Melamine will be available for the year. In addition, market constraints are expected to restrict the production and sales of each product to:

Modern: $5,000$ units, Antique: $4,000$ units, Trendy: $3,000$ units and Smart: $3,000$ units.

Required:

$($a$)$ Identify which product $($s$)$ the company should concentrate on$.$ Show all workings.

$(12$ marks$)$

$($b$)$ Calculate the numbers of each type of cabinets to be produced and sold to maximize profit of Modern Home Sdn Bhd$.$

$(10$ marks$)$

$($ c $)$ Prepare a marginal cost statement showing the profit of Modern Home Sdn Bhd for the year.

$(8$ marks$)$