PJ Construction Company produces two products, steel and wood beams.

Steel beams have a unit selling price of $$700,$ variable costs of $$400$ per unit and fixed costs of $$100$ per unit.

Wood beams have a unit selling price of $$500,$ variable costs of $$300$ per unit and fixed costs of $$80$ per unit.

The demand for steel beams exceeds PJ Construction Company's production capacity, which is limited by available direct labour and machine$-$hours. The demand for wood beams starts at a minimum of $4$ per week. Management desires that the product mix should maximize the weekly contribution margin toward fixed costs and profits.

Direct manufacturing labour is limited to $3,000$ hours a week and $1,200$ hours is all that the company's outdated machines can run a week.

The steel beams require $240$ hours of labour and $120$ machine$-$hours.

Wood beams require $300$ labour hours and $240$ machine$-$hours. a$.$ Set up the table, including data and constraints, needed to run solver. $(8$ marks$)$

Use solver to answer the following questions:

b$.$ Calculate the total contribution margin. $(2$ marks$)$

c$.$ If PJ can increase its total machinery hours to $1,440$ hours by purchasing new machines, what is the new contribution margin? What effect will this have on the company$$s overall profits, will they increase or decrease? By how much? Does the production of steel beams and wood beams change? By how much?

$($HINT $-$ Re$-$run solver$)(3$ marks$)$

d$.$ Identify two other factors that PJ should consider before deciding on whether to buy new machines. $($Make sure each of your answers is fully explained.$)(2$ marks$)$