Problem $8-12($Algo$)$

Alan Industries is expanding its product line to include three new products: $A,B,$ and $C.$ These are to be produced on the same production equipment, and the objective is to meet the demands for the three products using overtime where necessary. The demand forecast for the next four months, in hours required to make each product is:

$\backslash$table$[[$PRODUCT$,$APRIL,MAY,JUNE,JULY$],[$A$,780,580,780,1,180],[$B$,580,680,880,1,080],[$C$,680,480,680,830]]$

Because the products deteriorate rapidly, there is a high loss in quality and, consequently, a high carrying cost when a product is made and carried in inventory to meet future demand. Each hour's production carried into future months costs $$3$ per production hour for $A,$ $$4$ for $B,$ and $$5$ for $C.$

Production can take place either during regular working hours or during overtime. Regular time is paid at $$4$ when working on $A,$ $$5$ for B $,$ and $$6$ for C $.$ The overtime premium is $50$ percent of the regular time cost per hour.

The number of production hours available for regular time and overtime is

$\backslash$table$[[,$APRIL,MAY,JUNE,JULY$],[$Regular time,$1,480,1,350,1,780,2,000],[$Overtime$,680,630,880,1,000]]$

Calculate the objective value using Excel Solver.

Note: Do not round intermediate calculations.

$$

Objective value $$