This linear programming questions that found i operations research courses please solve it by hand with details

(4 Points) A furniture company manufactures desks and chairs. The maximum production capacity is estimated at either 80 desks or 150 chairs per day. The maximum daily demand is 60 desks and 120 chairs. The profit per desk is $70 and $45 per chair. Develop an LP model to determine the optimal daily production mix. ) (6 Points) The demand for ice cream at All-Flavors Parlor during the three summer months is estimated at 500, 600, and 400 cartons, respectively. The price per carton starts at $20 in the first month and increases by $1 each month thereafter. The supplier can provide no more than 400 cartons in any one month. Although we can take advantage of lower prices in early months, a storage cost of $3.80 is incurred per carton per month. In addition, the number of cartons that can be held over from one month to the next must be 80 or less. Develop an LP model to determine the optimum schedule for purchasing the cartons to meet the demand. (4 Points) A furniture company manufactures desks and chairs. The maximum production capacity is estimated at either 80 desks or 150 chairs per day. The maximum daily demand is 60 desks and 120 chairs. The profit per desk is $70 and $45 per chair. Develop an LP model to determine the optimal daily production mix. ) (6 Points) The demand for ice cream at All-Flavors Parlor during the three summer months is estimated at 500, 600, and 400 cartons, respectively. The price per carton starts at $20 in the first month and increases by $1 each month thereafter. The supplier can provide no more than 400 cartons in any one month. Although we can take advantage of lower prices in early months, a storage cost of $3.80 is incurred per carton per month. In addition, the number of cartons that can be held over from one month to the next must be 80 or less. Develop an LP model to determine the optimum schedule for purchasing the cartons to meet the demand