/4. A company manufactures doors in two factories, M and N. In each factory they produce both aluminium and timber doors of a standard size. The company must fill an order for at least 480 aluminium, and at least 600 timber doors. The daily running costs for factory M and N are $30 000 and $40 000 respectively. The daily production of these doors is given in the table. Factory Aluminium Timber M 40 70 N 80 60 Let x represent the number of days of operation of factory M, and y the number of days of operation of factory N. a. Write down the constraints on x and y. b. Graph the constraints on the same set of axes and find the feasible region. c. Write a linear relationship as an objective function for the total cost of production $C. d. For how many days should each factory operate to fill the orders, and minimise the costs involved in doing so? What is this minimum cost? 5. A company manufactures two different types of trucks, a one-tonne and a three-tonne model. Each week, they make a maximum of 550 one-tonners, and 400 three-tonners. Up to 125 workers are employed on the assembly line, each working a 38-hour week. The one-tonner requires 5 employee-hours of labour, while the three-tonner requires 8 employee-hours of labour for complete construction. The plant has enough parking spaces for up to 800 completed trucks. The company makes a profit of $14 000 on the one-tonner, and $15 000 on the three-tonner. Let x be the number of one-tonne trucks, and y the number of three-tonne trucks produced in a week. a. Write down the constraints on x and y. b. Graph these constraints on the same set of axes and find the feasible region. c. Write an equation for the profit $P, that the company can expect to make for x one-tonne trucks and y three-tonne trucks. d. Find the number of trucks of each type that the company should produce each week to maximise their profit, and find this maximum profit